  In this paper we present classes of state sum models based on the recoupling
theory of angular momenta of SU(2) (and of its q-counterpart $U_q(sl(2))$, q a
root of unity). Such classes are arranged in hierarchies depending on the
dimension d, and include all known closed models, i.e. the Ponzano-Regge state
sum and the Turaev-Viro invariant in dimension d=3, the Crane-Yetter invariant
in d=4. In general, the recoupling coefficient associated with a d-simplex
turns out to be a $\{3(d-2)(d+1)/2\}j$ symbol, or its q-analog. Each of the
state sums can be further extended to compact triangulations $(T^d,\partial
T^d)$ of a PL-pair $(M^d,\partial M^d)$, where the triangulation of the
boundary manifold is not keeped fixed. In both cases we find out the algebraic
identities which translate complete sets of topological moves, thus showing
that all state sums are actually independent of the particular triangulation
chosen. Then, owing to Pachner's theorems, it turns out that classes of
PL-invariant models can be defined in any dimension d.
