Why did many conquered peoples consider the Persians to be liberators?

Not many peoples thought so. First of all, the Jews. They were conquered by the Chaldean forces (or the New Babylonian kingdom). And King Navohodnezzar II ordered to overtake them to Babylon. This city at that time was the world center of culture and science. Representatives of many nations were herded there to concentrate knowledge. In addition, they were all related – the languages ​​were one, the Semitic group. And many have assimilated. Except for the Jews. After the conquest of the Persians, they were able to return home in a century. Many remained in Babylon. However, since the Jews wrote the Bible, they mentioned that Babylon was “the prison of the nations.”