If you can access them uning the POP, IMAP or SMTP protocols, you can have them all accessible at the same time when using an e-mail client like Thunderbird, outlook or some other client.
You may prefer using the IMAP or SMTP protocol for your business accounts to be able to access them from any of your computers. Those two leave the messages on the server.
If you use the POP protocol, all waiting messages will be transfered to your computer at once and revoved from the server every time you connect.
It's just a question of configuring the account to use the IMAP protocol, then to set up a local "account" for each one.
Once you are set, the 3 accounts will appear with any folders they may have. You can now start reading your e-mails from one account, pass to the next, and when all messages from the first account have been read, you'll be prompted to read the first message from the next account.
If you use Thunderbird, you'll have a side pannel showing all accounts with how many unread messages are available shown as "Inbox (n)".
Electro
February 2013