Using the propagation-circle and transform-circle graphic analysis, relation of axial-transfer to rotation, and then to axial-transfer has been developed and theoretically deduced based on axial-transfer invariability, which enriched the content of axial-transfer invariability. It was pointed out that the five-mirror cavity was a asymmetric cavity. And the design-scheme of modifying the five-mirror cavity to a nearly symmetrical cavity has been put forward based on axial-transfer to rotation to axial-transfer transform. As a result, the operation performance of the modified cavity was more stable.