There's a very explicit characterization of the derived equivalence -- in fact this is how Bridgeland CONSTRUCTS the flop (a really gorgeous idea IMHO). Namely you can build a very simple t-structure on D(Y) by a "tilting" procedure, and then the moduli of point objects is the flop Y^+. I forget the exact details but you do a tilt along the curve you want to contract, so that "perverse point sheaves" are just points away from this curve and are perverse coherent sheaves (in this case rank two complexes with H^0 being a line bundle and H^1 being torsion I think? the paper is great, so easy to find the precise statements).   The basic idea being that any derived equivalence (appropriately construed) can be characterized by a universal sheaf on the product, which you can interpret as saying the Y^+ will be a moduli of a particular family of objects in the derived category of Y -- so to build Y^+ you just need to say WHICH family of objects (and check some conditions).