The Troy and Greenbush Railroad was chartered in 1845 and opened later that year, connecting Troy south to Greenbush (now Rensselaer) on the east side of the Hudson River. The Hudson River Railroad was chartered on May 12, 1846, to extend this line south to New York City; the full line opened on October 3, 1851. Prior to completion, on June 1, it leased the Troy and Greenbush.

Cornelius Vanderbilt obtained control of the Hudson River Railroad in 1864, soon after he bought the parallel New York and Harlem Railroad.

In 1845, the Hartford and New Haven merged with the Hartford and Springfield Railroad to form the New Haven, Hartford and Springfield Railroad. The company reverted back to the Hartford and New Haven Railroad name in 1847.

The New York and New Haven Railroad (NY&NH) was a railroad connecting New York City to New Haven, Connecticut, along the shore of Long Island Sound. It opened in 1849, and in 1872 it merged with the Hartford & New Haven Railroad to form the New York, New Haven & Hartford Railroad. 

Wikipedia

The railroad  began as the Erie Railway, from 1861 to 1878.  Because of financial battles between Cornelius Vanderbilt and Jay Gould as well as the problem of a standard railroad gauge, the Erie went bankrupt and was reorganized as the New York, Lake Erie and Western Railroad.  By June of 1880, the railroad’s standard gauge conversion was completed.  The NY,LE&W RR lasted until 1893 when it too went bankrupt.  It was reorganized as the Erie Railroad.  Note the name change from Railway to Railroad.

The Lehigh Valley Railroad (reporting mark LV) was a railroad built in the Northeastern United States to haul anthracite coal from the Coal Region in Pennsylvania.

Buffalo, New York and Erie Railroad  Original Main Line  Erie Main Line at Corning  to Buffalo 41.6 miles (66.9 km)

Leased 1863 -  Created during the Erie's bankruptcy in 1858. Took over the Buffalo and New York City from Attica to Buffalo in 1859. Acquired the Buffalo, Corning and New York Railroad the same year and connected the two lines.

The New York and Erie Rail Road was chartered on April 24, 1832, by Governor of New York Enos T. Throop to connect the Hudson River at Piermont, north of New York City, west to Lake Erie at Dunkirk. On February 16, 1841, the railroad was authorized to cross into the northeast corner of Pennsylvania on the west side of the Delaware River, a few miles west of Port Jervis, NY, as the east side was already occupied by the Delaware and Hudson Canal to a point several miles west of Lackawaxen, PA.

Operated by the New York and Erie Railroad.  Runs between Horseheads and Watkins Glen.

The renamed Cleveland, Painesville and Ashtabula Railroad, March 31, 1868.

The Philadelphia and Trenton Railroad was a railroad from Philadelphia, Pennsylvania to Trenton, New Jersey. Opened in 1832, it became part of the Pennsylvania Railroad system in 1871.