A method for assembling an operating rig for a fluid in a body of water, of the type comprising the following steps: - bringing a buoy to the surface of the body of water substantially facing an anchoring region on the bottom of the body of water; - connecting a downstream point of a fluid transport pipe to the buoy; - completely immerging the buoy under the surface of the body of water before or after the connection step; - deploying in the body of water an intermediate section of the transport pipe from the downstream point to at least as far as an upstream point; the intermediate section being formed by a flexible pipe, the flexible pipe being capable of being wound and unwound reversibly without any significant plastic deformation on a drum or on a basket; - anchoring the upstream point on an anchoring element fixed on the bottom of the body of water in the anchoring region; - tensioning the intermediate section of the transport pipe between the downstream point and the upstream point under the effect of the buoyancy of the buoy, in order to maintain the intermediate section substantially vertical in the body of water; - connecting on the intermediate section a lower section intended to be connected to the bottom assembly and an upper flexible section intended to be connected to the surface assembly; characterized in that the buoy has a height, taken along a vertical axis (A-A') when the intermediate section is tensioned, of less than 1.5 time its maximum transverse dimension, taken transversely with respect to the vertical axis (A-A'), the step for bringing it comprising the displacement of the buoy between a remote position located away from the anchoring region and a placement position located facing the anchoring region, while maintaining the buoy partly immersed at the surface of the body of water, and in that the displacement of the buoy comprises towing of the buoy partly immersed in the body of water between its remote position and its placement position by at least one floating towing structure (92A, 92B). - bringing a buoy to the surface of the body of water substantially facing an anchoring region on the bottom of the body of water; - connecting a downstream point of a fluid transport pipe to the buoy; - completely immerging the buoy under the surface of the body of water before or after the connection step; - deploying in the body of water an intermediate section of the transport pipe from the downstream point to at least as far as an upstream point; the intermediate section being formed by a flexible pipe, the flexible pipe being capable of being wound and unwound reversibly without any significant plastic deformation on a drum or on a basket; - anchoring the upstream point on an anchoring element fixed on the bottom of the body of water in the anchoring region; - tensioning the intermediate section of the transport pipe between the downstream point and the upstream point under the effect of the buoyancy of the buoy, in order to maintain the intermediate section substantially vertical in the body of water; - connecting on the intermediate section a lower section intended to be connected to the bottom assembly and an upper flexible section intended to be connected to the surface assembly;