I think this is the one that has a couple of flights to go up and down (at least during the summer) and he doesn't want to hurt the pups growing bones/joints by jarring him up/down all the time.
Either hold his butt/back legs in one hand and his chest/front legs in the other and close to your chest OR hold his butt/back legs in the crook of your arm (elbow) and have him with his head over your shoulder or across your chest and in your other arm (kind of like holding a baby).
Going slow the dog won't do any damage - he can MINIMALLY go UP the stairs on his own, and can do SOME of the stairs. as long as he is walking, he will not do damage - just do not let him run up and down the stairs.
At 10 weeks Rexie fell down the stairs because of her oh-so-precise mastiff baby coordination. She wasnt even going fast the silly dufus. Im all about carrying pups down stairs, I just let her walk up, since you cant tumble up a staircase.