Compatibility of a US iphone 12 pro max in cyprus (european country)

Buying an iPhone in one country to use in another country can have many disadvantages:

Make sure it will work in your country! --> LTE Find the right iPhone for the right country or region. - http://www.apple.com/iphone/LTE/

and https://en.wikipedia.org/wiki/List_of_LTE_networks

Also check if your intended carrier requires a CDMA or GSM phone.

Some carriers will not accept unlocked phones - https://discussions.apple.com/message/20359060#20359060 - E.g., "Virgin Mobile, like all CDMA carriers, will only activate devices on their network that were initially sold for use on their network." and https://discussions.apple.com/message/33206605#message33206605 "The iPhone 7 and 7 Plus sold unlocked and for use on AT&T and T-Mobile is not physically compatible with the Verizon and Sprint networks."

If you can‘t make a FaceTime call on your iPhone, iPad, or iPod touch - https://support.apple.com/HT204168

November 2020 version "FaceTime isn't available or might not appear on [new] devices purchased in [...,] Pakistan, and United Arab Emirates, including Dubai."

Discounted phones sold in some US locations may be locked to a carrier. You have to complete the contract with the carrier before they will unlock the phone. In the end you are not saving money and may have to wait a long time. https://discussions.apple.com/thread/252444302?answerId=254609062022#254609062022

Other issues - https://discussions.apple.com/message/33176952#message33176952 - "The Japanese carriers are notoriously difficult to work with when it comes to unlocking. If you are not a customer of the carrier it's locked to, they will not unlock it."

Warranty restriction! - http://www.apple.com/legal/warranty/products/ios-warranty-document-us.html - "IMPORTANT RESTRICTION FOR iPHONE, iPAD AND APPLE TV SERVICE. Apple may restrict warranty service for iPhone, iPad and Apple TV to the country where Apple or its Authorized Distributors originally sold the device." <-- The warranty does not outright deny warranty coverage in other countries but there are many limitations to the effect Apple almost certainly will refuse to do repairs under warranty or even repairs at all except in the country of purchase. The device would have to be sent to a friend in the country of purchase to handle any repair claims because Apple will not handle international shipping.

Devices may also have tax added to the cost (e.g., in the USA prices do not include taxes), and you may have to pay import duty when bringing an expensive device into your country.

I am inviting you to spend the time doing the research using the links I provided. Either that or you will have to hope somebody from Cyprus who has experience with one happens by. I know nothing about the carriers on the island, or their requirements. I would have to spend an hour doing the research and I doubt they would all have pages in English, etc. As for things such as signal strength, that will depend also upon the carriers there and their towers, etc. In other words to get answers to all your questions would really require somebody intimately familiar with using a cellphone on Cyprus. If I were trying to find out I would try to find somebody who lived there to ask -- but wait -- you do don't you?!