Pluricanonical cohomology across flips

A flip can be thought of as a diagram X- --> X <-- X+ of complex threefolds satisfying some conditions. One often thinks of a flip as being in two par ts: the first part, X- --> X, is the given, while the second, X <-- X+, is the unknown. I calculate cohomological properties of the canonical classes, K- = Kx- and so on, and in particular properties of the function delta chi(mK) = X(X+, mK(+)) -- chi(X-, mK(-)). In the case of the toric hips of Danilov [3] and Reid [7], this function ca n be expressed in terms of lattice points of multiples of a polyhedron givi ng sharpness for the more general result.