A homogeneous batch of YBa2Cu3Ox porous ceramics was studied in detail as a function of the annealing temperature Ta. X-ray diffraction patterns and optical micrographs show definitely one single phase. Well-separated double superconducting transitions are, however, observed; most clearly in the specific heat curves, except for Ta≈460°C. Initial values are Tc1=87 K and Tc2=92 K for Ta=300°C. Upon increasing the annealing temperature Ta to 500°C, Tc1 increases to 93.5 K while Tc2 remains almost constant. Beyond Ta=500°C, both Tc1 and Tc2 decrease. The essentially reversible splitting of the superconducting transition appears to be due to the complex kinetics of the oxygen uptake. The two critical temperatures Tc1 and Tc2 are attributed to the high oxygen content external layer of the grains and to the low oxygen content grain cores, respectively.