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We present results from Path Integral Molecular Dynamics simulations that describe effects from the explicit incorporation of nuclear quantum fluctuations on the topology of the free energy associated to the geared exchange of hydrogen bonds in the water-water dimer. Compared to the classical treatment, our results reveal important reductions in the activation energy and changes at a qualitative level in the overall profile. Most notably are those manifested by a plateau behavior, ascribed to nuclear tunneling, that bridges reactant and product states, contrasting with the usual symmetric double well profile. This feature represents a clear The characteristics of the proton localizations along the pathway are examined. An imaginary time analysis of the rotational degrees of freedom of the partners in the dimer at the vicinities of the transition state shows a clear ``anticorrelation" between intermolecular interactions coupling beads localized in connective and dangling basins of attractions. As such, the transfer is operated by gradual concerted inter-basin migrations in opposite directions, at practically no energy costs. Modifications operated by partial deuteration and by theasymmetries in the hydrogen bonding characteristics prevailing in water-methanolheterodimers are also examined.