  We investigate the space-time regularity of the local time associated to
Volterra-L\'evy processes, including Volterra processes driven by
$\alpha$-stable processes for $\alpha\in(0,2]$. We show that the spatial
regularity of the local time for Volterra-L\'evy process is $P$-a.s. inverse
proportionally to the singularity of the associated Volterra kernel. We apply
our results to the investigation of path-wise regularizing effects obtained by
perturba\Ption of ODEs by a Volterra-L\'evy process which has sufficiently
regular local time. Following along the lines of [15], we show existence,
uniqueness and differentiablility of the flow associated to such equations.
