The questions “who maintains easement property?” is a bit too generic to have a simple answer.
The streets are located in “Public Rights of Way”. There is no clear title to that property, and it is available for adjoining property owners to gain access to their property. Utility companies can locate water/sewer/gas/telephone/and similar utilities. The City is responsible for the maintenance of the street paving if it is a dedicated/accepted street – if it is not pavement that has been accepted for maintenance then it is privately maintained. The Sanitation District is responsible for most storm sewer improvements. There are a considerable number of undeveloped rights of way (paper streets) in the City, and there is no entity responsible for the maintenance of undeveloped street rights of way. Yard areas in the right of way along dedicated streets are the responsibility of adjoining property owner to maintain. Dead trees in the ROW may be cut by the utility companies if they provide a danger to the overhead wires – the City may cut a tree if it falls on the roadway – however they will only cut it enough to restore traffic then the adjoining property owner is responsible for the remainder of the cleanup.
Dedicated Easements may have maintenance responsibility issues detailed in the easement document. Gas companies often keep their easement clear of trees and brush, and the sanitary sewer easements are often cut as well.