@native-api you are probably right in Testing multiple Ubuntu releases for multiple Python versions. I have a PyPI package I want to test.
So you suggest to use manylinux standard image with multiple Python versions, correct?
Would this be a good starting point? https://github.com/pypa/python-manylinux-demo
Or is there any resource which would be better to start with reading?
Yes, that looks like the example to start from. The .travis.yml syntax is a bit outdated (sudo: required is no longer needed and is now a no-op) but otherwise, it has all you need.
I also suggest to check out https://github.com/matthew-brett/multibuild which has richer built-in functionality for the same task: it supports all the Manylinux images and also PyPy, allows to build PyPI wheels for OSX and Windows as well and it can test the result, too.