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 E2 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.