Cash is managed through the regional branches of the Federal Reserve, and while there are some boundaries on that map that don't line up, it mostly seems to be governed by these particular administrative regions.
As a New Yorker from Connecticut, the gigantic barrier between New York and New England would have to be nearly completely explained by the Fed.
To expand on julespitt's comment: Each FRB (and whichever branches of each FRB has a cash department) gets money sent in from banks to be exchanged/counted/cleaned/recirculated/stored/whatever in whichever bank is closest. This explains a majority of these lines. This probably also explains why there's some really defined lines around Seattle, Denver, and Salt Lake City. Even though they are branches of FRB's, they still have cash departments.
Since most places you pay cash at take it straight to the bank ASAP for security reasons, most of your cash ends up at a bank. In fact, I'm having a hard time thinking of a business other than maybe a hotdog stand that doesn't take 100% of their cash revenues to the bank.
Businesses that collect large numbers of dollar bills bundle them up and give them to their banks, these wind up in the hands of the local federal reserve that checks them and delivers them to businesses that give out large numbers of dollar bills inside of the same district.