Spectral sequences of a Morse shelling

We recently introduced a notion of tilings the geometric realization finite simplicial complex and related those to discrete Morse theory R. Forman, especially when they have property be shellable, shared by classical shellable complexes. now observe that every such tiling supports quiver which is acyclic precisely then shelling induces two spectral sequences converge (co)homology complex. Their first pages are free modules over critical tiles tiling.