Changing network; not handset

Hi group,

I'm thinking of changing networks, whilst keeping my existing, unlocked, BlackBerry 9700.
I'm wondering if this will just be a simple SIM swap when the relevant contracts are stopped/started? I know I may need to tell the old network (Vodafone) to let go of my BB PIN and give it to the new network (Orange).
But what about e-mail? Will that automatically get delivered to my phone on the new network?

Any help appreciated - thanks!