Ok here it is complete.
DICLAIMER: It a proposal. Leoreth has the final word on tech tree.
EDIT: updated (here to avoid flooding the thread)
NOTE: Renaiscance era is completely reworked. Its changes won't be described below but in a separate section.
Requirements:
-Riding requires only pastorialism.
Reason: Riding should be researchable in parallel with chariots.
-Coinage requires mining.
Reason: Any metal is required to mine coins.
-Gunpowder doesn't require plow.
-Logistics require finance instead of cartography.
Reason: Logistics has to do more about maintainance which is a financial issue.
-Music requires only paper.
Reason: It isn't highly connected with the religious techs evangelism was involved.
-Microbiology requires biology.
-Refrigeration requires electricity, microbiology intead of fertiliser.
Reason: Electricity is required for heat pumps. Microbiology/vaccination/pastorisation justifies the nead for refridgeration.
-Agronomy requires microbiology and horticulture instead of biology.
Reason: Microbiology more suitable than Biology. Agronomy is the evolution of horticulture.
-Socialism requires biology instead of insurance.
Reason: Evolution is central in marxist and product philosophies.
-Healthcare doesn't require socialism
Reason: Deplex health and social concepts.
-Civil rights require socialism.
Reason: Connection with latest social science tech.
-Cement requires hydraulics instead of telephone
Reason: Cement making requires hydraulic systems, not electric systems.
-Control systems require electronics.
Reason: Electronics greatly developped this field.
-Tourism requires flight instead of aviation.
Reason: Flight merged with aviation.
-Semiconductors do not require cement.
-Lasers do not require fission.
-Rocketry requires pneumatics.
Reason: Rocketry requires control of fuel flaw.
Renamings:
-Record keeping renamed to Numbers.
Reason: All primitive writing systems were numbering systems. Number systems preexisted other kinds of writing.
-Plumbing renamed to hydraulics.
Reason: 1) It's the same thing in different language (Latin and greek). 2) It represents all the pneumatic and water systems of alexandrian era like archimedes water clock, justifying its connection to engineering.
-Mathematics to Geometry
Reason: 1) Given the requirements and results it represents geometry. 2) Differentiate from arithmetics that developped indepedently and before mathematics.
-Astronomy to astrology.
Reason: Release the name for modern astronomy.
-Navigation to astrolabe.
Reason: More specific name of a tech instead of a movement.
-Currency to Coinage
Reason: Potential differentiation of coins and paper money.
-Chivalry to Honour
Reason: More universal name that includes both european (chivalry) and far eastern concepts like Japanese warlords.
-Land tenure to vassalage
Reason: More specific and familiar name.
-Crop rotation to plow
Reason: One word name.
-Steam power to thermodynamics.
Reason: One word name, more generic and scientific.
-Feriliser to agronomy.
Reason: More generic and scientific name.
-Labour unions to socialism.
Reason: One word name. Includes marxist and product philosophies and political movements. Wider term than communism.
-Infrastructure to cement.
Reason: Better understanding of the tech in relation to its requirements.
-Space exploration to orbitics.
Reason: One word name. More generic and scientific.
-Mass media to television.
Reason: One word name. Name more consistent in relation to names with previous and next techs.
-Explosives to materials.
Reason: More generic and more suitable name given previous, next techs and what it enables.
Replacements:
-Jurisprudence replaced evangelism.
Reason: Evangelism is too specific to christianity. Juriprudence is a more universal concept that fits the requirements.
-Music replaced constitution.
Reason: Practically, constitution moved later on and music filled the gap. Magna Carta is represented by Jurisprudence
-Microbiology replaced representation and partially feriliser.
Reason: Practically, representation moved to renaiscance where it belongs. Microbiology appeared in industrial era where it belongs.
Microbiology represents vaccination and pastorisation, better than fertiliser.
-Control systems replaced aviation.
Reason: Control systems more suitable for 1) late military techs and 2) the techs former aviation led to. 3) Important tech that needs representation in the tech tree.
-Semiconductors replaced electronics.
Reason: Perfectly fits previous and next techs.
Merges:
-Hunting and leather working as Hunting.
-Carving and mining as Minings.
-Ceremonial burial and ritual as Ritual.
-Fishing, sailing and seafaring: practically Fishing and Sailing merged as Fishing, Seafaring renamed to Sails.
Reason: Ommit first coloumn.
-Flight and aviation as flight.
Reason: Same word in different languages english and french.
-Radio and electronics as electronics.
Reason: Radio is made with electronics.
Switches:
-Coinage and employment
Reason: Coinage has been developped before geometry.
-Gunpowder and logistics
Reason: Gunpowder belongs to medieval era. Logistics belong to renaiscance era.
Renaiscance era:
NOTE: the changes are many, so only important changes are noted here.
-Astronomy replaced metereology, it requires optics and leads to physics.
Reason: Suitable given the requirements and the leadings. Metereology is arguable.
-Hydraulics renamed to hydrodynamics.
Reason: Hydraulics means plumbing which is already present in the tech tree.
-Urban planning moved as requirement of hydrodynamics and requires optics and charter.
Reason: 1) Optics more suitable as requirement than constitution.
2) Urban planning more suitable as requirement of hydrodynamics than corporation and metereology/astronomy.
-Economics require charter. Corporation does not lead to hydrodynamics.
Reason: Economics developped after colonial empires.
-Sanitation removed.
Reason: See below
-Representation entered renaiscance era.
-Jurisprudence, civil liberties and nationhood are in inverse row.
Reason: Casuation and chronology.
-Constitution product of civil liberties.
Icon:
-Calendar took metereology icon, astrology took calendar icon, astronomy took astronomy icon.
Reason: The clouds are suitable for seasons, the stone carvings are suitable for astrology and coustelations suitables for astronomy.
-Microbiology took biology icon
Reason: Cells are suitable more for microbiology
-Biology took evolution icon
Reason: In this tech tree biology represents mainly evolution theory.
Effects:
-Logistics: Reduce unit maintainance by 35%
Reason: That's what logistics are for: Unit maintainance
-Electronics: +1

in hospitals
Reason: Radiological diagnosis devices.