A geometric description of the Atiyah-Hirzebruch spectral sequence for B-bordism

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.