An offshore drilling rig includes a drill deck, at least one work center arranged in the drill deck; a diverter system operatively connectable at least to a riser extending towards the seafloor; a hoisting system adapted for raising or lowering tubular equipment through the work center; wherein the offshore drilling rig includes a first positioning system configured for positioning at least the work center and/or the diverter system and/or a riser tensioning system selectively at a first horizontal position and a second horizontal position, different from the first horizontal position; and wherein the hoisting system is operable to raise or lower tubular equipment through the work center when said work center is positioned at said first horizontal position.