Thrust reverser comprising movable grids and cowls assembled by recessing

A thrust reverser for an aircraft propulsion unit, comprising a fixed portion, two cowls and deflection grids, each of the cowls being connected to the fixed portion according to a pivot connection so as to be able to be displaced between a closed position and an open position intended for the maintenance of the propulsion unit, the reverser comprising connecting means comprising one or several tabs formed by the cowls or respectively by the grids and at least one groove formed by the grids or respectively by the cowls, the connecting means being configured such that the tab(s) fit into the at least one groove when the cowls are displaced from the open position to the closed position such that, in the closed position, the cowls and the grids form a coupling which is movable relative to the fixed portion in translation along a longitudinal axis between an advanced position allowing the propulsion unit to generate a thrust and a retracted position allowing the propulsion unit to generate a counter-thrust, the coupling comprising tension members connected to the grids and being configured so as to exert a stress pressing the tab(s) into the at least one groove.