Fire III will cancel all stacks of Umbral Ice and give a full stack of Umbral Fire. Blizzard III will do the same in reverse. Transpose however will only grant one stack of the opposite buff, so it's best used to get a stack of mana regen at the end of a fight.
Blizzard III gets a cost and cast time reduction when you have three stacks of fire and will regen 80% of your mana in one tick. So usually you dump all mana in Fire with max stack > Blizzard III > Thunder > start fire cycle with full mana.