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We report on experimental studies of the character of phase transitions in the quasi-1D organic compound (TMTSF)2PF6 in the close vicinity of the borders between the paramagnetic metal PM, antiferromagnetic insulator AF, and superconducting SC states. In order to drive the system through the phase border P_0(T_0), the sample was maintained at fixed temperature T and pressure P, whereas the critical pressure P_0 was tuned by applying the magnetic field B. In this approach, the magnetic field was used (i) for tuning (P-P_0), and (ii) for identifying the phase composition (due to qualitatively different magnetoresistance behavior in different phases). Experimentally, we measured R(B) and its temperature dependence R(B,T) in the pressure range (0 - 1)GPa. Our studies focus on the features of the magnetoresistance at the phase transition between the PM and AF phases, in the close vicinity to the superconducting transition at T~1K. We found pronounced history effects arising when the AF/PM phase border is crossed by sweeping the magnetic field: the resistance depends on a trajectory which the system arrives at a given point of the P-B-T phase space. In the transition from the PM to AF phase, the features of the PM phase extends well into the AF phase. At the opposite transition from the AF to PM phase, the features of the AF phase are observed in the PM phase. These results evidence for a macroscopically inhomogeneous state, which contains macroscopic inclusions of the minority phase. When the system is driven away from the transition, the homogeneous state is restored; upon a return motion to the phase boundary, no signatures of the minority phase are observed up to the very phase boundary.