  We show that in anisotropic superconductors, falling at finite temperature
into the 3D-XY- and at zero temperature into the 2D-XY-QSI universality class,
the isotope effects on transition temperature, specific heat and magnetic
penetration depths are not independent, but related by universal relations. The
corresponding experimental data for cuprate superconductors reveals suggestive
consistency with these relations. They imply a dominant role of fluctuations so
that pair formation and pair condensation do not occur simultaneously. For this
reason and due to the occurrence of the 2D-XY-QSI transition the isotope
effects do not provide information on the underlying pairing mechanism but must
be attributed to a shift of the phase diagram upon isotope substitution. The
2D-QSI transition is driven by the exchange of pairs, which favors
superconductivity and the combined effects of disorder and Coulomb repulsion of
the pairs, which favor localization. Since isotope substitution will hardly
affect disorder and Coulomb repulsion, the shift of the phase diagram must be
attributed to the electron-phonon interaction, which renormalizes the mass of
the fermions and with that the mass and the exchange of the pairs.
