The Live Photos are a pair of a high resolution still frame and a short video clip with the animation.
When you transfer them from the iPhone to the Mac, you have to import the video clip and the still frame at the same time, and then Photos can combine them again to a Live Photo.
You can either transfer them using a USB connection and import from the iPhone this way (if the iPhone is not syncing with iCloud Photos) or letting them sync to the Mac with iCloud Photos.
But all this will not work properly, if you already have imported the still frames without the video component, for example from My Photo Stream, which will only transfer the still frame. Then the duplicate detection in Photos will prevent Photos from importing the pair of the still frame and the video together as a Live Photo. You would have to remove the still frames from the Photos Library and recently Deleted (or lonely video components, if you only imported the video) before you try to reimport the pairs combined to import the Live Photos properly.