Each day, the big three U.S. carriers provide 64 daily departures to Great Britain. They operate under an Open Skies agreement, negotiated between the U.S. and the European Union.

Were Great Britain to decide Thursday to exit the E.U., that agreement would have to be replaced. A new agreement would be likely, of course. No one wants to upset travel between two longstanding allies. Still, new negotiations always raise concerns -- which would be just one illustration of that anxiety that would be raised by a "Brexit."

"If U.K. leaves the E.U., it would mean the U.K. wouldn't be a part of the U.S.-E.U. Open Skies agreement," Wolfe Research analyst Hunter Keay wrote in a recent report. "We believe regulators would move quickly to hammer out a status-quo-like agreement on an interim basis until a new Open Skies agreement could be reached, but there's no guarantee that would be easy.

"We believe U.K. regulators have been tough negotiators in the past so it would be premature to say there'd be no incremental risks to the status quo, particularly if U.K. politics migrate to a more nationalistic, protectionist bend," Keay said. "Issues like foreign ownership restrictions could arise again, too."

Given that investors dislike uncertainty, the impact on airline shares would likely be negative. Airline shares are already having a bad year, the result of factors including not only the possibility of Great Britain's exit but also concerns over terrorism, rising fuel prices, falling load factors and the carriers' continued inability to produce positive revenue per available seat mile.

Year to date as of Monday's close, shares of American (AAL) - Get American Airlines Group, Inc. Report were down 30%; United (UAL) - Get United Airlines Holdings, Inc. Report was down 25% and Delta (DAL) - Get Delta Air Lines, Inc. Report was down 24%. In fact, among the nine largest U.S. airlines, the only winners were Spirit, up 10%, and Hawaiian, up 2%.

American has the largest exposure to the United Kingdom, according to Buckingham Research analyst Dan McKenzie. About 6.2% of American capacity touches the U.K., he said in a recent report, compared with about 5.3% of United capacity and 2.7% of Delta capacity. "We note that Delta's equity stake in Virgin {Atlantic} means the earnings at risk are larger" than the committed capacity, McKenzie noted.

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American offers an average of 25 daily summer departures to the United Kingdom, including flights to London Heathrow from Charlotte, Chicago, Dallas, Los Angeles, Miami, New York Kennedy, Philadelphia and Raleigh-Durham; flights to Manchester, England from Chicago; to Birmingham, England from JFK and Philadelphia; to Edinburgh, Scotland from JFK and to Glasgow, Scotland from Philadelphia. (Several flights operate more than once a day).

United offers 26 flights a day to the United Kingdom, including flights to Belfast, Northern Ireland from Newark; to Birmingham from Newark; to Edinburgh from Chicago and Newark; to Glasgow from Newark; to London Heathrow from Chicago, Los Angeles, Newark, San Francisco and Washington Dulles; to Manchester from Newark, Dulles and to Newcastle, England from Newark. (Among the busy routes, Newark-Heathrow has five flights a day). 

Delta offers 13 flights a day to the United Kingdom, including flights to London Heathrow from Atlanta (twice daily), Boston, Detroit, JFK (three times a day), Minneapolis, Philadelphia, Seattle and Salt Lake City; a flight to Edinburgh from JFK and a flight to Manchester from JFK.

McKenzie wrote that if Brexit is approved, he modeled -- for all three airlines -- "a 20% hit to U.K.-related revenue, a milder 10% hit to the euro mainland area, and a small hit to U.S. revenue, which resulted in a minus 17% impact to earnings for the Big 3. Specifically, our 2017 earnings outlook for AAL and UAL could fall roughly 20% and for Delta by 15%."

Nevertheless, McKenzie said he maintains buy ratings on the three carriers, despite the negative potential if Brexit is approved.

"Should the U.K. vote to remain within the E.U., we'd expect to see the stocks bounce somewhat given valuations that are a disconnect from their free cash flow stories (even though) near-term this summer sentiment likely remains poor given over capacity and weak pricing," McKenzie said.

This article is commentary by an independent contributor. At the time of publication, the author held no positions in the stocks mentioned.