Described is a method for deploying a stent-graft in the aorta, the method including positioning a shunt to go along a portion of a brain-supplying artery (BSA) into the aorta; deploying a stent-graft in the aorta along a portion of the shunt; and removing the shunt. Also described is a removable shunt adapted for deployment along a brain-supplying artery into an aorta to supply blood to the artery during deployment of a stent-graft in the aorta, the removable shunt including a stiff segment that is stiff enough to remain at least partially open when between the aorta and the stent-graft and large enough to allow sufficient blood supply to the brain during the deployment of the stent-graft; and a mechanism for facilitating safe removal of the shunt from between the stent-graft and the aorta. Also described is a method of deploying a branch stent graft having a flaring portion in a blood vessel branching at a bifurcation from an aorta to connect to an aortic stent graft deployed in the aorta across the bifurcation, a branch stent-graft useful in the method, and a delivery system useful in the method.