The present application relates to a compression stage of a low-pressure compressor of an axial turbomachine, such as a turboprop. The stage includes a rotor with, on its outer surface, two lip seals, each forming a radial annular rib; and a stator which includes an annular row of stator blades extending substantially radially; and an inner shell whose radial cross section includes a central part connected to the inner tips of the blades, a lateral part extending from each side of the central part to one of the two lip seals, respectively, thus forming a rotor with the annular cavity. The shell and the rotor are configured so that the radial section of the annular cavity has a length L1 and a height H, the length L1 being greater than the height H, which initiates rotational movement of the air contained therein. The speed of the air reduces its pressure, which limits downstream to upstream leaks.