  Elie Cartan's general equivalence problem is recast in the language of Lie
algebroids. The resulting formalism, being coordinate and model-free, allows
for a full geometric interpretation of Cartan's method of equivalence via
reduction and prolongation. We show how to construct certain normal forms
(Cartan algebroids) for objects of finite-type, and are able to interpret these
directly as infinitesimal symmetries deformed by curvature.' Details are
developed for transitive structures but rudiments of the theory include
intransitive structures (intransitive symmetry deformations). Detailed
illustrations include subriemannian contact structures and conformal geometry.
