An interesting opening in a game that I lost to a stronger opponent. Line we play says it gives a winning advantage to white, but I may have found a move that equalizes for black.  I'm black

I could not see black equalising at any stage Sorry to disagree with you However a good try indeed!

Before 19..Re8 I'm quite certain the game was at least equal if not to my advantage

I have to agree with vijay.  I think White holds the advantage throughout the game.

I agree with pvmike, Re8 was the turning point

After 13...Kxg7 white is down a pawn with little compensation, Could you guy's give some reasoning behind why white has the advantage.

This is not a new line. This is the Giuoco Piano transposed to the Max Lange Attack of the Two Knights Defense. 8.Re1+ is more popular, but 8.fxg7 is also played. 8.Re1+ makes things more complicated, although I think chances are fairly equal with correct play. 8.fxg7 gives black an easy game after 9...Be7. 9...f6 is obviously where black went wrong. Your book says advantage to white after 11.Bh6, and I agree. Where did you think you had equalized?

 

TO 

The new move I was talking about was 11...Bb4, up to that point all the moves are in my opening book. Which does say 9...f6 is a mistake, but I think 11....Bb4 equalizes.

Yes, your game seemed to improve after this move, but I think that is only because 12.Nbd2 is a poor move. 12.c3 seems to work out fine for white, although there is less chance for the advantage. I think 12.Re4 is the best move, and after this white is still doing quite well.

I'm looking at the line with 12.Re4 right now it does seems like white holds his advantage.

PVMIKE , since you feel 19...Re8 a mistake, just wondering what you see as the correct move there instead? It looks to me like WT has threats vs b7. And that for his next move some ideas: Ne6 being okay. But I'd prefer Rb3 or Qf3 as my serious candidates. So perhaps 19...Qd5 instead? Or the less active but somewhat prophylactic 19...Kh8 maybe to eliminate the N-fork SQ and hide the King from some potential checks?

19.Qd5 or 19.b6 are the moves I suggested in my original post. I think 19.Qd5 is best.