Celerity, alacrity, legerity are comparable when they are used in reference to human beings and denote quickness in movement or action.
Celerity stresses speed in moving or especially in accomplishing work.
Alacrity emphasizes promptness in response more than swiftness in movement, though the latter is usually implied. Very often, also, it connotes eagerness or cheerful readiness.
Legerity, a less common word than the others, refers more to the quality than to the rate of speed and implies nimbleness and ease.