Can the digitizer be removed without breaking?

It can be done but you will need to be very very careful it's also very easy to mark the glass on the inside and scrape away the white or black part of the glass

yes, We have done it. You can do it in all ipad types, 2, 3 , 4, mini's and ipad air. You have to heat up and then slowly make your way along the edges with heating consistently. Some people use some drops of super glue to attach the digitizer with the double sided tape. In these cases you will definitely break the digitizer.

Ipad air digitizers which we use come with original double sided glue.

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to remove these you will have no issues. Same goes for the ipad air's you need to open first time.

HEATING THE EDGES IS THE KEY. KEEP HEATING AND KEEP MOVING ALONG>

Like Ajaz said, it is possible. You need a temperature controlled heat gun, set to about 700 DF, and a good metal spudger to create an incision point on the corner of the device, and then about 8-10 guitar picks to slide gently around the perimeter of the digitizer, to de-adhere the glass from the frame. Time is on your side. Take your time, move slowly, and you should be ok.