Intersection homology of regular and cylindrical neighborhoods

We develop a spectral sequence for the intersection homology of regular neighborhoods in PL stratified pseudomanifolds and of certain cylindrical neighborhoods of pure subsets in homotopically stratified spaces. We also develop a theory of simplicial homology with stratified systems of local coefficients and show that the E 2 terms of our spectral sequences are computable in terms of the homology of the “base” space with a suitably defined stratified system of local coefficients.