Problems Deleting junk mail and slow updating.

I have several accounts set up in my Mac Mail, I have problems with the servers updating they are very, very slow as well as trying to delete and moving files. Sometimes when I delete or move the emails they disapear but then if I click on to another account then back again they are all back there, even when closing mail, resetting the computer it still does this, this happens on both my Mac Pro and MacBook Pro, I have 1 iCloud account, 4 Yahoo iMap Accounts and 1 Google iMap account and they all suffer from the same problem updating issues.

Any help would be greatly appreciated.

Many thanks

N.