carry over vs die hard

carry over and die hard both are verbs.

Word	Noun	Adjective	Verb	Adverb
carry over	No	No	Yes	No
die hard	No	No	Yes	No

As verbs, die hard is a hypernym of carry over; that is, die hard is a word with a broader meaning than carry over:

carry over: transfer or persist from one stage or sphere of activity to another
die hard: continue to exist

Other hypernyms of carry over include endure, persist, prevail, run.

carry over (verb)	die hard (verb)
transfer or persist from one stage or sphere of activity to another	continue to exist
transfer from one time period to the next
transport from one place or state to another
hold over goods to be sold for the next season