Carriers such as Ryanair, EasyJet and Wizzair are large Pan-European PLC's with no state ownership involvement. Local city region mayors have no role in dictating to them where they can and cannot operate. Even if they wanted to, it is unlikely that either (Manchester or Liverpool) mayors would wish to risk upsetting Ryanair or EasyJet - amongst the largest operators at both airports concerned. Wizzair does not currently base aircraft at either airport, but does operate a programme of visiting schedules at LPL.
Even in an unusual situation such as that we see at Teesside, the Mayor can offer incentive funds from his / her local budget to help attract new business to an airport. However, it is entirely at the discretion of the airline as to whether they want to take up the terms offered or not.