I was looking for a solution which wouldn't add any new dependencies. Check out the following (Python 3) solution:
class VersionManager:
    @staticmethod
    def compare_version_tuples(
            major_a, minor_a, bugfix_a,
            major_b, minor_b, bugfix_b,
    ):
        """
        Compare two versions a and b, each consisting of 3 integers
        (compare these as tuples)
        version_a: major_a, minor_a, bugfix_a
        version_b: major_b, minor_b, bugfix_b
        :param major_a: first part of a
        :param minor_a: second part of a
        :param bugfix_a: third part of a
        :param major_b: first part of b
        :param minor_b: second part of b
        :param bugfix_b: third part of b
        :return:    1 if a  > b
                    0 if a == b
                   -1 if a  < b
        """
        tuple_a = major_a, minor_a, bugfix_a
        tuple_b = major_b, minor_b, bugfix_b
        if tuple_a > tuple_b:
            return 1
        if tuple_b > tuple_a:
            return -1
        return 0
    @staticmethod
    def compare_version_integers(
            major_a, minor_a, bugfix_a,
            major_b, minor_b, bugfix_b,
    ):
        """
        Compare two versions a and b, each consisting of 3 integers
        (compare these as integers)
        version_a: major_a, minor_a, bugfix_a
        version_b: major_b, minor_b, bugfix_b
        :param major_a: first part of a
        :param minor_a: second part of a
        :param bugfix_a: third part of a
        :param major_b: first part of b
        :param minor_b: second part of b
        :param bugfix_b: third part of b
        :return:    1 if a  > b
                    0 if a == b
                   -1 if a  < b
        """
        # --
        if major_a > major_b:
            return 1
        if major_b > major_a:
            return -1
        # --
        if minor_a > minor_b:
            return 1
        if minor_b > minor_a:
            return -1
        # --
        if bugfix_a > bugfix_b:
            return 1
        if bugfix_b > bugfix_a:
            return -1
        # --
        return 0
    @staticmethod
    def test_compare_versions():
        functions = [
            (VersionManager.compare_version_tuples, "VersionManager.compare_version_tuples"),
            (VersionManager.compare_version_integers, "VersionManager.compare_version_integers"),
        ]
        data = [
            # expected result, version a, version b
            (1, 1, 0, 0, 0, 0, 1),
            (1, 1, 5, 5, 0, 5, 5),
            (1, 1, 0, 5, 0, 0, 5),
            (1, 0, 2, 0, 0, 1, 1),
            (1, 2, 0, 0, 1, 1, 0),
            (0, 0, 0, 0, 0, 0, 0),
            (0, -1, -1, -1, -1, -1, -1),  # works even with negative version numbers :)
            (0, 2, 2, 2, 2, 2, 2),
            (-1, 5, 5, 0, 6, 5, 0),
            (-1, 5, 5, 0, 5, 9, 0),
            (-1, 5, 5, 5, 5, 5, 6),
            (-1, 2, 5, 7, 2, 5, 8),
        ]
        count = len(data)
        index = 1
        for expected_result, major_a, minor_a, bugfix_a, major_b, minor_b, bugfix_b in data:
            for function_callback, function_name in functions:
                actual_result = function_callback(
                    major_a=major_a, minor_a=minor_a, bugfix_a=bugfix_a,
                    major_b=major_b, minor_b=minor_b, bugfix_b=bugfix_b,
                )
                outcome = expected_result == actual_result
                message = "{}/{}: {}: {}: a={}.{}.{} b={}.{}.{} expected={} actual={}".format(
                    index, count,
                    "ok" if outcome is True else "fail",
                    function_name,
                    major_a, minor_a, bugfix_a,
                    major_b, minor_b, bugfix_b,
                    expected_result, actual_result
                )
                print(message)
                assert outcome is True
                index += 1
        # test passed!
if __name__ == '__main__':
    VersionManager.test_compare_versions()
EDIT: added variant with tuple comparison. Of course the variant with tuple comparison is nicer, but I was looking for the variant with integer comparison