  We construct a many-body quantized invariant that sharply distinguishes among
two dimensional non-equilibrium driven phases of interacting fermions. This is
an interacting generalization of a band-structure Floquet quasi-energy winding
number, and describes chiral pumping of quantum information along the edge. In
particular, our invariant sharply distinguishes between a trivial and anomalous
Floquet Anderson insulator in the interacting, many-body localized setting. It
also applies more generally to models where only fermion parity is conserved,
where it differentiates between trivial models and ones that pump Kitaev
Majorana chains to the boundary, such as ones recently introduced in the
context of emergent fermions arising from eigenstate $\Z_2$ topological order.
We evaluate our invariant for the edge of such a system with eigenstate $\Z_2$
topological order, and show that it is necessarily nonzero when the Floquet
unitary exchanges electric and magnetic excitations, proving a connection
between bulk anyonic symmetry and edge chirality.
