What is the alternative to using --process-dependency-links with pip

You can use PEP 508 URL requirements:

pip @ https://github.com/pypa/pip/archive/19.2.3.zip

They'll work for direct requirements (via the CLI, or listed in requirements.txt) and packages that aren't downloaded by pip from PyPI. Note that support for this was released in pip 18.0 (i.e. early 2018, because pip's on CalVer now).

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In OP's case, the requirements.txt can be unchanged (though, they'd want to remove --process-dependency-links), if the dependency links are updated to the PEP 508 format.