Unfortunately for the early Christians, it was the Romans who were in power. Most of the time, Christians could live in peace as long as they didn't go out of their way to antagonize Romans with their "superstitious" behavior, but by the mid-third century, some emperors thought sacrifice to the gods was essential to the welfare of Rome. Christians, of course, refused to participate in such rites. During the periods when the Romans actively sought out Christians, Christians could recant and offer sacrifices or face an unpleasant death sentence. Sentencing to the arena to face the wild and hungry animals was one such sentence. They might otherwise be sent to the mines (damnatio ad metallum). Exile was a possibility. Some would recant after a period of imprisonment and torture.
The persecutions of the Christians refer to times when they were actively sought out and punished, generally starting with the fixing the blame for the fire in Rome on Christians during the reign of Nero.
References:
"persecutions, early Christian" The Concise Oxford Dictionary of the Christian Church. Ed. E. A. Livingstone. Oxford University Press, 2006.
Persecution in the Early Church
