Manchester Airport is a major employer in the area, being two thirds owned by ten boroughs of Greater Manchester and employing 19,000 people directly as well as supporting a further 42,500 jobs in the north west. A large part of the airport's growth is down to EU regulations which have encouraged growth and competition in air travel between EU member states. In particular, the Open Skies Directive (which can be thought of as a "single market for air travel") has benefitted UK airlines and as a result major national and international airports such as Manchester. The Open Skies Directive permits airlines from any member state to operate services throughout the EU, not only to and from an airline's home country but between any other EU member states or even within those member states. So for example, British Airways could operate not just Manchester to Bucharest flights but also Madrid to Berlin and Milan to Naples if the market would stand it. UK airlines can sell tickets to anyone in the 28 member states of the EU with no bureaucratic hurdles. As a result the UK has the largest aviation network in Europe and the third largest in the world. The rise of EasyJet to become the UK's largest airline is a direct result of the lowering of barriers to competition that EU legislation has enabled. Consumers have benefitted from this enhanced competition: air fares across the EU have dropped by around 40% in real terms and new routes have opened up across Europe. Outside of this EU framework, there is no fallback regime for European air transport and unless a UK-EU agreement was quickly negotiated, there would be no legal framework for flights from the UK to the EU (there is no World Trade Organisation equivalent ruleset to fall back on, unlike in the case of international trade of goods).
It is also European legislation that has brought compensation for passengers if flights are delayed and the right to hotel accommodation in case of significant delay. Clearly, this kind of legislation requires concerted action by different national governments otherwise airlines would just base themselves in countries that did not have these kinds of rules. But the agreements at EU level to create more than just the ability for UK airlines to fly new routes across Europe; it is via the EU that the UK has a similar "open skies" agreement with the US which has been largely responsible for the growth in transatlantic flights. In particular this EU-US agreement has allowed for US flights to UK airports outside London such as Manchester; outside the EU the UK would be required to fall back on the 1977 Bermuda Agreement which was far more restrictive and only allowed US-UK flights to and from London airports (at the behest of the UK which feared the market power of US airlines would dominate the sector if unrestricted). As with many other issues relating to international affairs, the UK on its own is at a disadvantage because of our inability to stand up to larger countries: if we "club together" with our European neighbours and partners we can make agreements that better suit our needs than if we try to negotiate on our own. The direct economic benefits to Manchester, its environs and its residents are clear.
Richard Corbett MEP has an article discussing the many negative effects that leaving the EU will have on the UK aviation sector, both in terms of consumer choice and protection but also legal regulation of aircraft safety and air traffic control. It is a very complex topic where leaving the EU without a deal on going forward will leave UK airlines and passengers with a massively restricted choice of routes, no or much-reduced consumer protection laws and uncertainty for air freight forwarding regulations from airports such as Manchester (particularly if we leave the EU customs union). This issue was never discussed during the referendum campaign, but is it really what we voted for?