In condensed matter physics, the search for new exotic quantum ground states has become a central theme over the past few years. Among the 3D quantum spin liquid candidates, the rare-earth pyrochlore Yb2Ti2O7 stands out as a very promising one since its lowest Kramers doublet is characterized by XY symmetry and is well separated from the first excited one, giving rise to strong quantum fluctuations with an effective Seff=1/2 moment. Recently, several studies have revealed the dramatic impact of a minute off-stoichiometry x, in Yb2+xTi2-xO7, on its ground state. We now aim at following the evolution of the spin dynamics using inelastic neutron scattering in clean and controlled Yb2(Ti1-xZrx)2O7 samples, going from the pure, x=0, ordered sample through the intermediate region towards the critical, non-magnetic, phase as x increases.