  We deal with stochastic differential equations with jumps. In order to obtain
an accurate approximation scheme, it is usual to replace the "small jumps" by a
Brownian motion. In this paper, we prove that for every fixed time $t$, the
approximate random variable $X^\varepsilon\_t$ converges to the original random
variable $X\_t$ in total variation distance and we estimate the error. We also
give an estimate of the distance between the densities of the laws of the two
random variables. These are done by using some integration by parts techniques
in Malliavin calculus.
