We report results of magnetization measurements on the same YBa 2 Cu 3 O 7Ϫ␦ crystal for a range of ␦ values 0.03р␦р0.35, in magnetic fields up to 120 kOe, applied parallel or perpendicular to the CuO 2 planes.Zero-field resistivity anisotropy measurements have also been made for the same values of ␦. The irreversibility line H irr falls by over a factor of 10 in the range of ␦ studied, and there is a similar strong decrease in superconducting condensation energy associated with the growth of the normal-state pseudogap in underdoped cuprates. On the other hand, the anisotropy in H irr and the room-temperature resistivity anisotropy only increase by a factor of 2. Evidence that for our crystals the so-called ''vortex lattice melting line'' H m (T) ϷH irr (T) is presented. There is also a large field and temperature region where the reversible magnetization varies as H Ϫ1/2 and its magnitude corresponds to a free-energy density of k B T in a certain field-dependent correlation volume. Many of the results are consistent with the presence of critical thermodynamic fluctuations described by the three-dimensional XY model; these are probably enhanced when the field along the c axis is greater than 10 kOe. ͓S0163-1829͑99͒02825-8͔ CHANGES IN IRREVERSIBILITY LINE, . . .