Question: Let's say user A follows user B, and B follows A. I want to know the exact date A started following B and viceversa.
Is this information stored on twitter? Can I retrieve it using the API?

To clear out: The point of this question is finding a way to know who followed who first.
(I'm assuming both A and B deleted the notification e-mails)

Answer: 
No Ignacio, you can't. You just can know who follows who but not the date the follow started.

Looking at the API, there's is no way, there are two calls to get the followers:

User Methods/statuses/followers

and

Social Graph Methods/followers/ids 

Neither of them returns dates or even a serial that would let you see who started following first. Really, **there's no indication that twitter is internally storing this information**, neither in the API nor Twitter's web interface.
Of course Twitter stores it, because Twitter sorts followers and following lists by the date ;)