I got the following line drawing in Illustrator.
How to import a SVG without closing the curves?
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The closed curve is called Cyclic, to open and close a Cyclic go into Edit Mode and hit the hotkey Alt+C.
If you are open to installing a blender add-on, you might want to give this one a try: Blender Add-on to Import Shape Keys
It appears to have quite a few import options.