I bought an AMP machine earlier this year and my lad, who is more interested in the detail than me, tells me that in his experience, after the 4th or so firing, annealing prevents/reduces springback after resizing - so the resized case remains the size as it was after being resized. Specifically referring to Lapua 6.5 CM cases.

I now anneal after every firing, to ensure consistency, and as it is a very quick process it's no hassle.