  In this paper we give a geometric description of the general term and the
differential of the Atiyah-Hirzebruch spectral sequence for $B$-bordism. This
description is given in terms of bordism classes of maps from stratifolds. We
illustrate that with a computational example. We also discuss the case of a
general homology theory, where this description is given in terms of the
Postnikov sections of the given theory.
