  The covariant Gromov-Hausdorff propinquity is a distance on Lipschitz
dynamical systems over quantum compact metric spaces, up to equivariant full
quantum isometry. It is built from the dual Gromov-Hausdorff propinquity which,
as its classical counterpart, is complete. We prove in this paper several
sufficient conditions for convergence of Cauchy sequences for the covariant
propinquity and apply it to show that many natural classes of dynamical systems
are complete for this metric.
