A carcass ply is applied around an outer surface of a building drum, according to an application diameter greater than the fitting diameter of the tire. An annular anchoring structure defining the fitting diameter is coaxially engaged around each of the end flaps. An outer sleeve including at least one belt structure possibly associated with a tread band is disposed at a coaxially centered position around the carcass sleeve applied onto the building drum. Through axial approaching of two halves forming the building drum, the carcass sleeve is shaped into a toroidal configuration to determine application of same against a radially internal surface of the outer sleeve.