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International audienceWe give an explicit bound for the $L_1$-distance between two additive processes of local characteristics $(f_j(\cdot),\sigma^2(\cdot),\nu_j)$, $j = 1,2$. The cases $\sigma =0$ and $\sigma > 0$ are both treated. We allow $\nu_1$ and $\nu_2$ to be equivalent time-homogeneous Lévy measures, possibly with infinite variation. Some examples of possible applications are discussed

$L_1$-distance for additive processes with time-homogeneous Lévy measures