  We construct a covering of Culler-Vogtmann Outer space by the Teichmuller
spaces of punctured surfaces. By considering the equivariant homology for the
action of Out(F_n) on this covering, we construct a spectral sequence
converging to the homology of Out(F_n) that has E^1 terms given by the homology
of mapping class groups and groups that are, up to finite index, subgroups of
mapping class groups. This spectral sequence can be seen as encoding all of the
information of how the homology of Out(F_n) is related to the homology of
mapping class groups and their subgroups.
