CHAMP1"Redirect" normally implies re-sending the messages to an alternative receiving address.
However, in TB you also have the choice of telling each account where to store its messages, and you can nominate account A's inbox, for instance, to be where account B places received messages. And there is the Global Inbox, where all POP accounts share the same set of folders, and there is Unified folders view which creates a virtual composite set of folders, so all of your messages, POP and IMAP, appear to be in the one set of folders.
You may also be able to set up a forward or redirect on the other account's webpage, so that the redirecting is done by the email provider's server and doesn't need to involve TB at all.
If person A sends mail to B, and B forwards it to C, then to C it will appear to have come from B, not A. OTOH, if B redirects to C, it still appears to have come from A. Watch out for this; if your server offers forwarding as opposed to redirecting, you may lose the context of messages.
There is a "Redirect" add-on for TB, but I don't know of any way to fire it off from a Message Filter, which would be the obvious way of automating this process.
Oh, and while I've never used it, I believe gmail has a feature whereby you can set it to access other accounts on you behalf. So rather than pushing other accounts' messages into gmail, you get gmail to pull them in. Go look at your gmail settings page on the web.