A method for maintaining a constant bottom hole pressure during wellbore drilling operations, the method comprising supplying drilling fluid to the drill string via a top drive at a first pressure while flow of drilling fluid out of a wellbore annulus is restricted by a choke to hold pressure in a wellbore annulus and supplying drilling fluid to the drill string via the top drive at a second pressure lower than the first pressure and to a circulation coupler at a third pressure while flow of drilling fluid out of a wellbore annulus is restricted by a choke to hold pressure in the annulus, wherein the sum of the second and third pressures is approximately the same as the first pressure. The method also comprises supplying drilling fluid to the drill string via the circulation coupler at the third pressure while pumping drilling fluid into the wellbore annulus by a back pressure pump, wherein the bottom hole pressure at the bottom of the wellbore is maintained substantially constant during all steps of supplying drilling fluid to the drill string.