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We establish the global asymptotic equivalence between a pure jumps L\'evyprocess $\{X_t\}$ on the time interval $[0,T]$ with unknown L\'evy measure$\nu$ belonging to a non-parametric class and the observation of $2m^2$ Poissonindependent random variables with parameters linked with the L\'evy measure$\nu$. The equivalence result is asymptotic as $m$ tends to infinity. The time$T$ is kept fixed and the sample path is continuously observed. This resultjustifies the idea that, from a statistical point of view, knowing how manyjumps fall into a grid of intervals gives asymptotically the same amount ofinformation as observing $\{X_t\}$.

Asymptotic equivalence of jumps L\'evy processes and their discrete counterpart