The exchange and inelastic state-to-state cross sections, for the OH+ + H collisions are computed from wave packet calculations using the doublet and quartet ground electronic, potential energy surface (PES) correlating to the Open shell reactants, for collision energies in the range of 1 meV to 0.7 eV. The doublet PES presents a deep insertion well, of approximate to 6 eV, but the exchange reaction has a rather low probability, showing that the mechanism is not statistical. This well is also responsible of a rather high rotational energy transfer, which makes the rigid-rotor approach overestimate the cross section for low Delta j transitions and for high collisonal energies. The quartet PES, with a much shallower well, also present's a low exchange reaction cross section, but the inelastic state-to-state cross sections are very well reproduced by rigid-rotor calculations. When the electronic partition is used to obtain the total state-to-state cross section, the,contribution of the doublet state becomes small, and the resulting total cross sections become close to those obtained for the quartet state. Thus, the total (quartet and doublet) cross sections for this open shell system can be reproduced rather satisfactorily by those obtained with the rigid-rotor approximation on the quartet state. Finally, we compare the new OH+-H cross sections with OH+-He ones recently computed. We found significant differences, especially for transitions with large Delta j showing that specific OH+-H calculations had to be performed to accurately analyze the OH+ emission from interstellar molecular clouds.