Yuriy T/Getty Images Avoiding a full trial over disputed costs and work quality on the Mario M. Cuomo Bridge in New York could save tens of millions of dollars—if a settlement is reached. Rival legal teams have reached a critical juncture as they consider a mediated settlement in one of two major lawsuits pending between a design-build contracting team and the New York State Thruway Authority over construction of the $3.1-billion Mario M. Cuomo Bridge in New York. The design-build contractors are seeking about $930 million in unpaid costs from the T hruway Authority.  The authority says it faces tens of millions in costs in replacing defectively installed cable stay anchors on the bridge. The bridge, which crosses the Hudson River 15 miles north of New York City, replaced the 50-year-old Tappan Zee Bridge. The design-build team, known as Tappan Zee Constructors, is  composed of Fluor Corp., Granite Construction Inc., Traylor Bros. Inc. and American Bridge Co.…