Hall measurements are usually performed to obtain information about the material mobility and charge carrier density. However, in transition-metal oxides, continuous Hall measurements are quite scarce. We present a continuous Hall measurement across the metal-insulator transition (MIT) in VO2, which undergoes a drastic change in resistance of 4 orders of magnitude around 340K. In the high-resistance regime even small misalignment of the contacts results with a significant offset that screens the Hall signal. Our continuous measurement was possible using the reciprocity relation , that implies that instead of changing field polarity one can simply measure at two different configurations that removes the zero-field offset. Using that switching method we were able to change slowly and continuously the temperature and measure the pure Hall signal along it. The surprising results show a difference of over 1 order of magnitude between resistivity and Hall resistance. Such a change is naively regarded as a change in mobility. We were able to prove by applying the exact relation theory that the mobility is almost constant, and that the discrepancy is due to the VO₂ spatial phase separation across the MIT.