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We experimentally investigate the sensing properties of an open cavity operating in the THz regime and realized by employing as mirrors two thin vanadium dioxide (VO2) films grown on silicon parallel plates and separated by a variable length. The phase transition of VO2 is used to control the behavior of the system between two different responses: a high transmission mode to the incident radiation (VO2 in the insulating state) and a high sensitivity to tiny changes in the cavity refractive index (VO2 in the conducting state). In the first state, the low loss regime enables to adjust the cavity length and easily optimize the resonances due to the Fabry-Perot (FP) effect in the Si plates and in the cavity volume. The activation of the metallic-like state instead, by damping the FP oscillations in the plates, promotes the onset of a comb-like spectrum that can be exploited as a versatile tool for accurate sensing applications. Using both an analytical model and full-wave simulations, we estimate the device response to variation in the refractive index of the cavity volume, showing that the proposed structure can achieve sensitivity values among the highest reported for THz sensors.