Only two airlines - Avianca and LATAM Airlines - have international subsidiaries and cover many destinations within the Americas as well as major hubs in other continents. LATAM with Chile as the central operation along with Peru, Ecuador, Colombia, Brazil and Argentina and formerly with some operations in the Dominican Republic. The AviancaTACA group has control of Avianca Brazil, VIP Ecuador and a strategic alliance with AeroGal.

Codesharing is the most common type of airline partnership; it involves one airline selling tickets for another airline's flights under its own airline code. An early example of this was Japan Airlines' (JAL) codesharing partnership with Aeroflot in the 1960s on Tokyo–Moscow flights; Aeroflot operated the flights using Aeroflot aircraft, but JAL sold tickets for the flights as if they were JAL flights. This practice allows airlines to expand their operations, at least on paper, into parts of the world where they cannot afford to establish bases or purchase aircraft. Another example was the Austrian–Sabena partnership on the Vienna–Brussels–New York/JFK route during the late '60s, using a Sabena Boeing 707 with Austrian livery.
Groups such as the International Civil Aviation Organization establish worldwide standards for safety and other vital concerns. Most international air traffic is regulated by bilateral agreements between countries, which designate specific carriers to operate on specific routes. The model of such an agreement was the Bermuda Agreement between the US and UK following World War II, which designated airports to be used for transatlantic flights and gave each government the authority to nominate carriers to operate routes.
You seem to have your heart set on Zakynthos but I have to say it’s not a good use of time for a sort-of overrated payoff. Your time is much better spent (in my opinion) seeing another Greek island in the cyclades (maybe taking a ferry to Naxos or Paros sitting outside on the deck drinking a bottle of wine) rather than taking a bus and connecting flights. Zakynthos and Santorini/Mykonos are on opposite sides of the country and the only way from one to the other is by flying (or some combination of bus and ferry). So, my recommendation is to consider spending those Zakynthos days in Naxos, Paros, Milos, or some other Cycladic island.

Unlike its luxurious Caribbean neighbors, here you’ll only find more budget-friendly hotels and guesthouses. Everything needs to come by ship or airplane, so it’s not super cheap. However, since no non-natives can own property there is no influx of overdevelopment, keeping the island simple but beautiful. For a more rustic, non-touristy getaway, this might be the island for you!

If a particular city has two or more airports, market forces will tend to attract the less profitable routes, or those on which competition is weakest, to the less congested airport, where slots are likely to be more available and therefore cheaper. For example, Reagan National Airport attracts profitable routes due partly to its congestion, leaving less-profitable routes to Baltimore-Washington International Airport and Dulles International Airport.

A more recent development is the airline alliance, which became prevalent in the late 1990s. These alliances can act as virtual mergers to get around government restrictions. Alliances of airlines such as Star Alliance, Oneworld, and SkyTeam coordinate their passenger service programs (such as lounges and frequent-flyer programs), offer special interline tickets, and often engage in extensive codesharing (sometimes systemwide). These are increasingly integrated business combinations—sometimes including cross-equity arrangements—in which products, service standards, schedules, and airport facilities are standardized and combined for higher efficiency. One of the first airlines to start an alliance with another airline was KLM, who partnered with Northwest Airlines. Both airlines later entered the SkyTeam alliance after the fusion of KLM and Air France in 2004.
By the end of the 1930s Aeroflot had become the world's largest airline, employing more than 4,000 pilots and 60,000 other service personnel and operating around 3,000 aircraft (of which 75% were considered obsolete by its own standards). During the Soviet era Aeroflot was synonymous with Russian civil aviation, as it was the only air carrier. It became the first airline in the world to operate sustained regular jet services on 15 September 1956 with the Tupolev Tu-104. 

Thus the last 50 years of the airline industry have varied from reasonably profitable, to devastatingly depressed. As the first major market to deregulate the industry in 1978, U.S. airlines have experienced more turbulence than almost any other country or region. In fact, no U.S. legacy carrier survived bankruptcy-free. Among the outspoken critics of deregulation, former CEO of American Airlines, Robert Crandall has publicly stated:

Crete, Santorini, and Naxos look quite doable within the 12-day block, but Crete’s beaches are scattered throughout a very LARGE island, Santorini really only has Kamari and Perissá (and some southern coast bays) and Naxos does have nice places to swim. If you choose only to visit those three islands in your relatively short time, you will do well.
In recognition of the essential national economic role of a healthy aviation system, Congress authorized partial compensation of up to $5 billion in cash subject to review by the U.S. Department of Transportation and up to $10 billion in loan guarantees subject to review by a newly created Air Transportation Stabilization Board (ATSB). The applications to DOT for reimbursements were subjected to rigorous multi-year reviews not only by DOT program personnel but also by the Government Accountability Office[46] and the DOT Inspector General.[47][48]