Can I use the floating mana durning the battle step or does it dissapear when going into the battle step?
It will have disappeared by then, unfortunately. Here's your ruling:
500.4. When a step or phase ends, any unused mana left in a player's mana pool empties. This turn-based action doesn't use the stack.
RESOLVED
The mana disappears when you enter your combat phase unless its green mana and you have {Omnath, Locus of Mana} then you can float mana
Thanks