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First your mail server needs to be IMAP and support push mail.

Go into Mail » Preferences » Accounts (Advanced) and make sure that Use IDLE command if the server supports it is enabled (it's enabled by default).

(This is the fun part) Again go into Mail » Preferences » General and set Check for new Mail to Manually.

Now send yourself a new message (preferably from a different account) and watch the fun.

From this Link
 
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