I believe the crane at the Broadway is a self-assembling tower crane so they can lift it to the proper height when they need to. It usually take a few guys and a couple of hours to lift it but I've seen cranes get raised an extra 100 feet in a day.
kinda like this.
that is where the slewing unit(tower) is detached from the mast(upper arm and pivot.)
then hydraulic lifts raise the slewing unit up twenty feet so a new section can fit.
then they just push it in there, assemble it and repeat the process.
found these pics at
How Stuff Works.