Officials smashed a wall with sledgehammers to celebrate the start of the work.
Civic leaders are trying to reclaim an area they say was usurped by planners years ago.
Renovations are expected to begin this August after Billy Joel plays the arena's last concert.
The deal is subject to NHL approval.
Voters will decide whether Suozzi or Haber win the Democratic primary Tuesday to face Mangano in November.
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