would

The Western Roman Empire crumbled in the fifth century as it was overrun by invading Germanic tribes. However, the once great empire had already undergone significant changes. It had been divided into western and eastern empires, and its capital had moved east from Rome to the Greek city of Byzantium. The city would become known as Constantinople after the emperor Constantine, who made it the new capital in A.D. 330. (Byzantium would remain as the name of the entire Eastern Empire.) For nearly a thousand years after the collapse of the Western Empire, Byzantium and its flourishing capital would carry on the glory of Rome.

What does the three 'would's mean grammatically respectively?