  We provide a simple proof of the topological invariance of the Turaev-Viro
model (corresponding to simplicial 3d pure Euclidean gravity with cosmological
constant) by means of a novel diagrammatic formulation of the state sum models
for quantum BF-theories. Moreover, we prove the invariance under more general
conditions allowing the state sum to be defined on arbitrary cellular
decompositions of the underlying manifold. Invariance is governed by a set of
identities corresponding to local gluing and rearrangement of cells in the
complex. Due to the fully algebraic nature of these identities our results
extend to a vast class of quantum groups. The techniques introduced here could
be relevant for investigating the scaling properties of non-topological state
sums, being proposed as models of quantum gravity in 4d, under refinement of
the cellular decomposition.
