Looking at the Animal Shapes spell (PHB pg.212) it says:

On subsequent turns, you can use your action to transform affected creatures into new forms.

Followed by the usual transformation rules:

• They revert to their original form if they drop to 0 HP or die.

• Excess damage is carried over if they revert to their original form.

• Their stats are replaced with the stats of the new form, save for Int, Wis, and Char scores.

• They assume the hit points of the new form etc.

Given that it says nothing about damage being carried over from one form to another and "they assume the HP of the new form", it would certainly seem that each time the creature is transformed it is also essentially healed of any damage it may have taken in its previous form.

Is this correct? Does a creature get a new, full pool of HP with each transformation or does the damage it takes in one form carry over to the new one?