The general rule would be that you are responsible for maintaining the easement in a passable/usable condition unless the easement itself provides something different. You need to find that document (it may be in your deed or may be recorded separately) and review it. If it is not clear, you need to talk to an attorney.
Start by reading the document under which you obtained the rights.
In most cases, easements do not create obligations on the owner of the underlying property. However, roads are a common exception: the costs for maintenance are more often set forth in an easement.
You would be well advised to bring the document to an attorney for review.
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