  We aim at reviewing and extending a number of recent results addressing
stability of certain geometric and analytic estimates in the Riemannian
approximation of subRiemannian structures. In particular we extend the recent
work of the the authors with Rea [19] and Manfredini [17] concerning stability
of doubling properties, Poincar\'e inequalities, Gaussian estimates on heat
kernels and Schauder estimates from the Carnot group setting to the general
case of H\"ormander vector fields.
