  The barrier crossing event for superdiffusion in the form of symmetric
L\'{e}vy flights is investigated. We derive from the fractional Fokker-Planck
equation a general differential equation with the corresponding conditions
useful to calculate the mean residence time of a particle in a fixed interval
for an arbitrary smooth potential profile, in particular metastable, with a
sink and a L\'{e}vy noise with an arbitrary index $\alpha$. A closed expression
in quadrature of the nonlinear relaxation time for L\'{e}vy flights with the
index $\alpha =1$ in cubic metastable potential is obtained. Enhancement of the
mean residence time in the metastable state, analytically derived, due to
L\'{e}vy noise is found.
