  Intersection homology is a topological invariant which detects finer
information in a space than ordinary homology. Using ideas from classical
simple homotopy theory, we construct local combinatorial transformations on
simplicial complexes under which intersection homology remains invariant. In
particular, we obtain the notions of stratified formal deformations and
stratified spines of a complex, leading to reductions of complexes prior to
computation of intersection homology. We implemented the algorithmic execution
of such transformations, as well as the calculation of intersection homology,
and apply these algorithms to investigate the intersection homology of
stratified spines in Vietoris-Rips type complexes associated to point sets
sampled near given, possibly singular, spaces.
