I would like some help from people who understand cat body language or have introduced new cats.

The tabby is my male cat who has been my only cat for over a year, we got him as a stray kitten (probably about 8 weeks old) so we suspect, as my husband said "he dosnt know how to cat" this is the only other cat he has ever met.

The black cat is new, she is a pregnant female and was dropped of at my grandma's house and interacted with her colony.

What I would like to know is what you guys think is happening here. She has a room that I keep her in most of the time for now until they can get along and I put them together, supervised for a few minuets at a time. There is lots of growing and the occasional swat but for the most part they sit about 3 feet away and dont move. From what I understand a cat rolling over and bearing his belly is a sign of trust. Is this a breakthrough or am I just not understanding? This is day 3 with her by the way.