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We consider non-degenerate SDEs with a $\beta$-Holder continuous and boundeddrift term and driven by a Levy noise $L$ which is of $\alpha$-stable type. If$\alpha \in [1,2)$ and $\beta \in (1 - \frac{\alpha}{2},1) $ we show pathwiseuniqueness and existence of a stochastic flow. We follow the approach of[Priola, Osaka J. Math. 2012] improving the assumptions on the noise $L$. Inour previous paper $L$ was assumed to be non-degenerate, $\alpha$-stable andsymmetric. Here we can also recover relativistic and truncated stable processesand some classes of temperated stable processes.

Stochastic flow for SDEs with jumps and irregular drift term