Transfer to the US from Europe

Hi, I was working in M&A advisory at a BB for two years and have now been doing internal/ corporate M&A for another two years at another BB in London. I have been wanting to move to the US for some time and asked to transfer to the NY office of my bank which I would prefer but the chances aren't very high.

I am therefore looking at opprtunities outside the bank to get a job in New York and was wondering if anybody had ideas how to best approach this. I don't have many headhunter contacts over there but was thinking about sending my CV to a couple of them. Also not sure how big of an issue working permits/ Visa are (I am an EU citizen).

Any advice from people who've been in this situation or know of somebody who has done a similar move is highly appreciated.

Thanks!