  In this paper, we study the positive cross curvature flow on locally
homogeneous 3-manifolds. We describe the long time behavior of these flows. We
combine this with earlier results concerning the asymptotic behavior of the
negative cross curvature flow to describe the two sided behavior of maximal
solutions of the cross curvature flow on locally homogeneous 3-manifolds. We
show that, typically, the positive cross curvature flow on locally homogeneous
3-manifold produce an Heisenberg type sub-Riemannian geometry.
