  The Vlasov equation is used to determine the dispersion relation for the
eigenmodes of magnetized nuclear and neutral stellar matter, taking into
account the anomalous magnetic moment of nucleons. The formalism is applied to
the determination of the dynamical spinodal section, a quantity that gives a
good estimation of the crust-core transition in neutron stars. We study the
effect of strong magnetic fields, of the order of $10^{15}-10^{17}$ G, on the
extension of the crust of magnetized neutron stars. The dynamical instability
region of neutron-proton-electron ($npe$) matter at subsaturation densities is
determined within a relativistic mean field model. It is shown that a strong
magnetic field has a large effect on the instability region, defining the
crust-core transition as a succession of stable and unstable regions due to the
opening of new Landau levels. The effect of the anomalous magnetic moment is
non-negligible for fields larger than 10$^{15}$ G. The complexity of the crust
at the transition to the core and the increase of the crust thickness may have
direct impact on the properties of neutrons stars related with the crust.
