  We present a novel idea for a coupling of solutions of stochastic
differential equations driven by L\'{e}vy noise, inspired by some results from
the optimal transportation theory. Then we use this coupling to obtain
exponential contractivity of the semigroups associated with these solutions
with respect to an appropriately chosen Kantorovich distance. As a corollary,
we obtain exponential convergence rates in the total variation and standard
$L^1$-Wasserstein distances.
