  In this paper we study global distance estimates and uniform local volume
estimates in a large class of sub-Riemannian manifolds. Our main device is the
generalized curvature dimension inequality introduced by the first and the
third author in \cite{BG1} and its use to obtain sharp inequalities for
solutions of the sub-Riemannian heat equation. As a consequence, we obtain a
Gromov type precompactness theorem for the class of sub-Riemannian manifolds
whose generalized Ricci curvature is bounded from below in the sense of
\cite{BG1}.
