There's no bloom filters involved, or any actual attempt at synchronization. Nodes relay transactions they hear about to one another there's probably some level of consistency in mempool contents but no guarantee. If there was no mempool, there would be no way for miners to learn about unconfirmed transactions to include in blocks to begin with.

There's no bloom filters involved, or any actual attempt at synchronization. Nodes relay transactions they hear about to one another, so there's probably some level of consistency in mempool contents but no guarantee. If there was no mempool, there would be no way for miners to learn about unconfirmed transactions to include in blocks to begin with.