  We analyze the stability of generic spherically symmetric thin shells to
linearized perturbations around static solutions. We include the momentum flux
term in the conservation identity, deduced from the ''ADM'' constraint and the
Lanczos equations. Following the Ishak-Lake analysis, we deduce a master
equation which dictates the stable equilibrium configurations. Considering the
transparency condition, we study the stability of thin shells around black
holes, showing that our analysis is in agreement with previous results.
Applying the analysis to traversable wormhole geometries, by considering
specific choices for the form function, we deduce stability regions, and find
that the latter may be significantly increased by considering appropriate
choices for the redshift function.
