Darkness and Dawn

A Classic sci-fi trilogy.
The Vacant World - Beatrice Kendrick, and her boss, engineer Allan Stern, wakes up on an upper floor of a ruined Manhattan skyscraper, thousands of years in the future when civilization has been destroyed. The pair has been in a state of suspended animation for fifteen hundred years. Changes in the earth's features as well as monstrously mutated "humans" make it clear they have little hope of survival.
Beyond the Great Oblivion - Allan and Beatrice begin to discover the nature of the catastrophe that has split the Earth open. Rebuilding an airplane, they find a "bottomless" chasm near Pittsburgh where a huge portion of the Earth has been torn away to become a second moon. Alan and Beatrice earn the loyalty of the People of this Abyss and lead them from the chasm to New York.
The Afterglow - Allan and Beatrice, with the People of the Abyss, prepare to recolonize the Earth's surface. But first, they must defeat the devolved, cannibalistic survivors who populate Earth's cities.