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1.
When a husband and wife share a birthday and then get married on their birthday.
Katie and Greg share a birthday and then got married on their birthday. This day is now their annibirthary.
by gmoney625 June 25, 2012
 
2.
The anniversary of one's birth.

Interesting way of saying 'birthday'.
Today is my annibirthary, I hope I get lots of presents and cake!
by hafofme April 15, 2010