  We develop a variational theory of geodesics for the canonical variation of
the metric of a totally geodesic foliation. As a consequence, we obtain
comparison theorems for the horizontal and vertical Laplacians. In the case of
Sasakian foliations, we show that sharp horizontal and vertical comparison
theorems for the sub-Riemannian distance may be obtained as a limit of
horizontal and vertical comparison theorems for the Riemannian distances
approximations.
