  We analyse the spectral edge regularity of a large class of magnetic
Hamiltonians when the perturbation is generated by a globally bounded magnetic
field. We can prove Lipschitz regularity of spectral edges if the magnetic
field perturbation is either constant or slowly variable. We also recover an
older result by G. Nenciu who proved Lipschitz regularity up to a logarithmic
factor for general globally bounded magnetic field perturbations.
