  We establish direct isomorphisms between different versions of tiling
cohomology. The first version is the direct limit of the cohomologies of the
approximants in the Anderson-Putnam-G\"ahler complex, the second is the
recently introduced PV-cohomolgy of Bellissard and Savinien and the third is
pattern equivariant cohomology. For the last two versions one can define weak
cohomology groups. We show that the isomorphisms extend to the weak versions.
This leads to an alternative formulation of the pattern equivariant mixed
quotient group which describes deformations of the tiling modulo topological
conjugacy.
