A finiteness theorem for transitive foliations and flat vector bundles

In this paper we prove a finiteness theorem for the spectral sequence (E _i(∇), (d _∇)_i) associated to a transitive foliation on a compact manifoldM, and to a flat vector bundleE overM with flat connection ∇. we also compute some examples of homogeneous Lie foliations on compact connected homogeneous spaces.