  D.Sullivan (1977) (see also the book by H.Whitney "Geometric Integration
Theory",1957) considered a new model for underlying cochain complex for
classical cohomologies with rational coefficients for arbitrary simplicial
spaces that gives the isomorphism with classical rational cohomologies. We
apply the key ideas developed by K.MacKenzie (2005) and J.Kubarski (1991) to
generalization of the D.Sullivan model for transitive Lie algebroids. The
generalization is based on the existence of the inverse image of the transitive
Lie algebroids and on the property of transitive Lie algebroids being trivial
over contractible manifolds. Using these properties one can construct an
underlying cochain complex of differential forms on simplicial space.
