  We show that the vanishing of the higher dimensional homology groups of a
manifold ensures that every almost CR structure of codimension $k$ may be
homotoped to a CR structure. This result is proved by adapting a method due to
Haefliger used to study foliations (and previously applied to study the
relation between almost complex and complex structures on manifolds) to the
case of (almost) CR structures on open manifolds.
