Flash
Flying
You may cast colorless spells and artifact spells as though they had flash.
Whenever you cast a spell, if the amount of mana spent to cast that spell is greater than Liberator, Urza's Battlethopter's power, put a +1/+1 counter on Liberator.
The last ability cares only about the amount of mana that was actually spent to cast the spell, regardless of its mana cost.
The third ability applies only to casting spells. It does not, for example, change when you may activate abilities that can be activated "only as a sorcery."