For the ancient era: what do people think of having the first column be 'Prehistory'? It's defined as 'the period before written records', and all of the first column techs have to do with social advances that we know through archaeological (rather than written) records. 'Late Neolithic' works as well, since it applies to any society before the rise of metallurgy, and smelting is a second-column tech. OTOH, 'Stone Age' fits really neatly into a pattern for the rest of the ancient era (Stone Age -> Copper Age -> Bronze Age).
EDIT: alternately, instead of 'Copper' Age (based on the fairly obscure technical term Chalcolithic) we could borrow from Age of Empires and use 'Tool Age' for the second column. 'Proliferation of tool usage' certainly fits a column that includes the 'Masonry', 'Smelting', and 'Leverage' techs.
Really like 'Axial Age' for the middle column of the Classical period. Not as much a fan of 'Imperial Age' for the third Classical column, since that seems too Rome-centric to apply across the globe. 'Classical Antiquity' is somewhat generic, but it works for pretty much every world culture of that time.
For medieval techs: 'Late Antiquity' probably works best for the first column, since it's a historically meaningful term that covers the whole 400-800 CE period. 'High Medieval' fits the middle column. Ironically, from what I can tell, 'Renaissance' is actually the best name for the third column, since gunpowder & printing press & humanism all properly belong to that period.
If we do use 'Renaissance' as a name for a 'medieval' tech column (which would be accurate, since the Renaissance properly dates to the years around 1450), then the next set of three would be 'Early Modern' instead. 'Age of Exploration' fits for the first column, though I'd suggest 'Age of Absolutism' for the second -- that period marks the rise of absolute monarchies and authoritarian governments the world over, which partly inspired the rise of classical liberalism and egalitarianism (and the whole 'Age of Revolutions') as a backlash.
For the Industrial era, steam power preceded the widespread proliferation of railroads, which in turn preceded the Second Industrial Revolution that produced electricity, the internal combustion engine, telecommunications, and flight.
For the Global era, I'd actually argue for 'Modern Age' as a specific term for the first column here. This is the period associated with 'modernist literature', modernist philosophy (hence the name 'post-modernism' for philosophers who disagreed), 'modern art', 'modern warfare', the rise of modern psychology, etc.
Finally, for the Digital era, the first column matches the general pattern of the 'Computer Revolution' (Age of Computing?), while we seem to be living in the early stages of the second column as the 'Information Age'. the last column fits pretty perfectly to the definition of the 'Singularity' as a concept in futurism: with a Unified Theory of Everything, and true Artificial Intelligence... well, there are no more brakes on this train.
Honestly, looking over the list... it really does depend on how much Leoreth wants to maintain consistency. Most of the ancient/classical columns fit the '____ Age' model, many of the modern columns are 'Age of _____', and everything in the middle is a free-for-all.
Ancient Era
- Stone Age
- Copper Age
- Bronze Age
Classical Era
- Iron Age
- Axial Age
- Classical Antiquity ?
Medieval Era
- Late Antiquity ?
- High Medieval Age ?
- Renaissance / Late Medieval Age?
Early Modern Era
- Age of Exploration
- Age of Absolutism
- Age of Revolutions
Industrial Era
- Age of Steam
- Age of Rail
- Age of Electricity / Industrial Revolution
Global Era
- Modern Age
- Atomic Age
- Space Age
Digital Era
- Computer Age
- Information Age
- Singularity