Using two cold-neutron triple-axis spectrometers we have succeeded in fully mapping out the field-dependent evolution of the non-reciprocal magnon dispersion relations in all magnetic phases of MnSi. The non-reciprocal nature of the dispersion manifests itself in a full asymmetry (non-reciprocity) of the dynamical structure factor S(q, E, mu H-0(int)) with respect to flipping either the direction of the applied magnetic field mu H-0(int), the reduced momentum transfer q, or the energy transfer E. (c) 2018 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).