The width in temperature of the reversible, lossy state of high-temperature superconductors (HTS s) in a magnetic field H depends on the degree of anisotropy. Compared to the parent compound YBa2Cu307, we show here that oxygen-deficient, YBa2Cu307y single crystals, in which T, was varied from 10 to 55 K, are much more anisotropic and that the occurrence of the reversible, lossy state for the H~~c axis is consistent with a crossover from three-dimensional (3D) vortex lines to 2D vortices, as

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... ntly proposed for the other highly anisotropic HTS's. These results, together with those from T12Ba2CaCu20 and Bi2Sr2CaCu&0", indicate universal behavior of almost isolated Cu-0 bilayer units, albeit with different doping levels, and which display magnetic reversibility controlled by the residual weak interplanar coupling.