An attachment arrangement at a middle of a cover having an elastically deformable portion. The cover includes a concave shell including an inner surface spaced apart from the compressor including an impeller including blades by an attachment. The attachment includes one connection end at the middle of the shell, another end attached to a casing of the turbine engine, and an axisymmetric diaphragm having a generally frusto-conical configuration having an arm profile coupled to the end for attachment to the casing by a double-elbow joint having right and obtuse angles when in a rest position. The distance between the inner surface of the shell and upper edges of the blades can be held constant during operation with minimum clearance adjustment. The cover can be moved such that clearance between the cover and blades of the compressor impeller remains substantially constant and as low as possible.