  We study the convergence in distribution of the supremum of the local time
and of the favorite site for a transient diffusion in a spectrally negative
L\'evy potential. To do so, we study the h-valleys of a spectrally negative
L\'evy process, and we prove in partiular that the renormalized sequence of the
h-minima converges to the jumping times sequence of a standard Poisson process.
