I have seen some pictures and videos in the web about the so-called "Double Lineman s loop" - which, geometrically / structurally, is a very different knot. Now, if one can do some "magic" transformation, and show how the one can be turned into the other ( without un-tucking and re-tucking the eyes of the loop, of course, because, if we allow such transformations, we can start from any TIB double loop and end to any other !

), I would be happy to see it, because, if it exists, it is not obvious to me. Some people can "see" such transformations at once, and some others not - and I am afraid I belong to those who can not.
P.S. Noope ! Although it is incredible in how many different stable forms can each of those two loops be dressed, I have not managed to transform the one into the other. What am I missing ?