Ok, I fixed it. there was "input<M,w)" which some how confused the editor or something, some spaces and changing ")" to ">" seem to have solved the issue. Thank you Reeshabh for bringing it to my attention.

The answer is complete, but for some reason it's concealed. If I try to edit the answer I see it all, but when I save it then all words after ", given input" disappear.

I want to try and prove $OVERLAP_{TM}$ is $RE$ (Turing Recognizable). We do this by defining a TM $K$ that will recognize the language: on Input $M_{1} , M_{2}$ simulate them on words of their input non deterministically and accept if they both accept. (Is this a valid proof!?)

Sorry, I revised the question.