score:4
The status of Byzantium most probably changed in 47AD, just somewhat, because of the Roman Bosporan War of emperor Claudius. After reading more about the conflict, I doubt there was any "annexation". Instead, the trend looks quite the opposite. The city probably got more freedoms after contributing heavily to the war effort.
[During the Bosporan War] Byzantium [was] burdened with the significant tribute and possibly the sea carrying of Thracian cohorts and their supplies as the course of history of heavy burdens of this town has shown. Tacitus asserts that the inhabitants of Byzantium were exhausted by the late war in the Bosporus, so their tribute had been remitted by Claudius for five years (Tac., Ann. XII, 63)