Can you cast spells or activate abilities between the two parts of a double-faced card's transform trigger?

When a double-faced card transforms, it does so as a single, indivisible game action. There is no moment between the front face ceasing to exist and the back face appearing where any player could cast spells or activate abilities. The transform instruction is executed completely before anyone receives priority again (CR 701.28a).

The key principle is that instructions on a resolving spell or ability are carried out fully before the game checks state-based actions and before players receive priority (CR 608.2). Transforming is one of those instructions — it isn't split into two separate events that create a window in between.

It's also worth noting that transform doesn't cause the permanent to leave the battlefield; it stays on the battlefield and simply changes which face is up (CR 701.28b). Because the permanent never leaves and re-enters, there is no 'between' moment analogous to a blink effect where timing windows could open.

Concrete example: Suppose Delver of Secrets triggers and you reveal an instant, so it transforms into Insectile Aberration. Your opponent cannot respond to the 'flip' by trying to kill the creature while it is still a 1/1 Delver — by the time anyone gets priority after the trigger resolves, it is already a 3/2 Insectile Aberration.

Priority is only returned to the active player after the entire triggered ability has fully resolved, including the transform instruction (CR 608.2b, 117.3b). So there is simply no legal timing window to act between the two parts of the transformation.