  We investigate the physical meaning of some of the texture zeros which appear
in most of the Ansatze on leptonic masses and their mixing. It is shown that
starting from arbitrary lepton mass matrices and making suitable weak basis
transformations one can obtain some of these sets of zeros, which therefore
have no physical content. We then analyse four-zero texture Ansatze where the
charged lepton and neutrino mass matrices have the same structure. The four
texture zeros cannot be obtained simultaneously through weak basis
transformations, so these Ansatze do have physical content. We show that they
can be separated into four classes and study the physical implications of each
class.
