Once the basic structure of the trade center was in place, work proceeded at a fast clip. Three floors could be constructed in ten days.
As work continued, between the mid-sixties and early-seventies, sixty construction workers were killed. No PATH (Port Authority Trans-Hudson) train was ever rerouted, and PATH service was never disrupted, because of the building project.
This documentary was made, in 1983, by The Port Authority of New York and New Jersey.
It contains footage of the twin towers during their construction years - from the mid 60s through the early 70s.
Port Authority documentary, part two.