“Magic” — to inspire it in audience members and dancers of all ages is the perennial achievement of “The Nutcracker” at the New York City Ballet as it celebrates its 75th anniversary this year. 

When the sparkling Christmas tree on stage soars to forty feet, children in the audience gasp. Some even shed a tear. The Nutcracker toy, gifted to the tale’s heroine, Marie, during the opening party scene, soon comes to life as a little prince. What follows in choreographer George Balanchine’s two-act staging, performed every year since 1954, is a series of fantastical events and curious characters in the dreamworld of Marie and her prince.