carry through
Continue with or persevere to the end, as in She carried the project through despite being ill. Shakespeare used this idiom in king Lear (1:4): "My good intent may carry through itself." [c. 1600]
Survive or persist, as in His excellent technique carries through all his work.
Also, carry one through. Enable to endure; sustain. For example, His faith helped carry him through this last ordeal. [Mid-1700s]