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A systematic investigation of the magnetization reversal processes is carried out for the single epitaxial Co(111) nanowires possessing step-induced magnetic anisotropy with the easy direction of magnetization oriented perpendicular to the long wire axis. Wires of varying width (500-1800 nm) were patterned by focus ion-beam etching. We separated 3 regions of the NW width: the first is characterized by dominating step-induced magnetic anisotropy, in the second shape anisotropy prevails and in the third two anisotropies are in competition. We establish experimentally mechanisms of the magnetization reversal in the Co(111) nanowires in the directions of magnetic field parallel and perpendicular to the long wire axis in each separated region.