How are you rendering animations in Unity?
If you are using spine-unity then setting the position of the Spine gameobject corresponds to the world 0,0 position and your animations will all use the same reference point.
Are you exporting images and rendering frame-by-frame animations? There are two ways to solve this:
You can place a transparent image in Spine that is the maximal bounds of all your animations. When you export images, they will all have that common size. Whitespace stripping when packing an atlas removes the blank space.
Another way to do the same is to check Maximal bounds
when exporting your images, but then you need to export ALL your images at once. With the transparent image, you can export a single animation with maximal bounds.
The second solution is that when exporting an image sequence and packing it into an atlas, the world origin is written to the atlas file for each frame. It appears in the atlas data as origin
and has an X and Y value. If you draw all your images using the origin as an offset, they will be positioned relative to the same point and frames won't jump around.
FWIW, most Spine users are using spine-unity, as that provides the many benefits of skeletal animation.