Process for manufacturing a plastic hollow body, the process comprising the following steps: a) a tubular stream of molten plastic is extruded; b) this stream is taken up by means of a tensioning device; c) a transverse cut is made in this stream so as to create a parison having one free edge that is not taken up by the tensioning device; d) the parison is moved relative to the tensioning device so that the free edge of the parison is also taken up by the tensioning device; and e) at least one longitudinal cut is made in the parison over its entire length. Equipment suitable for implementing this process.