This story starts off at the end of Chapter 47 when Eren was hauled off by the Armoured Titan with Bertholdt and Ymir ((and Christa)).
They got away, and the Police and the Scouts lost sight of them. Levi was sent in along with a handful of others for backup.
Mikasa crouches down, her back facing him in a ready position. "Climb on."
He is stunned but it doesn't take him awhile to respond with a negative answer.
She gets up and faces him. "With all due respect, sir, I think it's best if we conserve our gas and use mine instead. Plus, your leg hadn't fully healed yet. I take full responsibility for what happened and what's going to happen to you, sir... Please, let me do my job, sir."
He is moved but hesitates. He is set on his ways, and takes orders from no one except his superiors. He pulls rank and says, "I made, make, and will make my own choices, soldier."
They stand in an impasse, neither budging, both reluctant, and too stubborn to give in.
After the subsequent standoff, Mikasa reverts back to her former crouching position and remains unmoving.
He exhales and says in the firmest voice, "I am no dead weight, soldier."
"I am not at all implying that, sir, but the others have long left and we're losing daylight here, sir."
He thinks that too, and decides to give this round to her. He gets on Mikasa's back with a heavy heart and she waits until he's settled in.
She puts on the hood of her Scouting Legion coat and maneuvers through the forest deftly and with no apparent difficulty. Her otherwise billowing black hair is contained inside the hood but her ever present red scarf sneaks its tail out for the passenger to see. Levi plays with the threads of the red scarf thoughtfully.
The trip is a silent one but not awkwardly so. They both treasure their own personal space and what with the current situation lacks of, makes up with the private solace in each mind.
It is a long trip and Levi couldn't help but feel distressed. Nobody, not a girl or man, carried him before. He is sure he is quite heavy despite his short stature and that his own 3D Maneuver Gear is additional baggage. He wants so badly to get off of her and travel on his own.
And if she's feeling burdened, she does not show it. She is panting, which is understandable as it has been a long trek) and he can feel her heart beating loudly but she showed no sign of slowing down.
If she hasn't earned his respect before, she surely has now.