I updated the draft “Orderings of filters in terms of reloids. Extensions of Rudin-Keisler ordering” at this Web page.
In the updated version reloids between different sets (I now call them trans-reloids.) are considered in a formal manner, unlike a somehow informal approach in the previous version of this draft. Instead of proving all properties of trans-reloids directly I managed to reduce some properties of trans-reloids to properties of plain reloids. So there are no necessity to reproduce the entire theory of reloids for the more general case of trans-reloids.
This draft is essentially complete, but little errors in the proofs are possible.
I hope to make the final draft soon.