I believe Dras has already quoted all the relevant passages, and I fully agree with him.
The term "increase" is never defined in the rulebook, or explicitly differentiated from the term "add". "Battery" and "Attack Pool", on the other hand, are.
Having said that, since " adding to the attack pool" is well defined and gets its own timing step, using a different term for the battery is good design practice as it avoids confusion:
"Increase your battery armament by 1 red die" is clear and unambiguous.
"Add 1 red die to your battery armament" is also, in my opinion, clear and unambiguous and means the exact same thing, BUT it could easily result in some people (incorrectly) arguing that the timing for adding of dice to the pool should apply here as well.
Does that mean that "increase" and "add" are operative keywords? Not really. But it's just better to avoid confusion.
Edited by DiabloAzul