Railroads connecting New York City and Chicago
In the "Official Territory", the land of the Northeast U.S. bounded roughly by the Mississippi, Ohio and Potomac rivers, one of the most important railroad corridors is between New York City and Chicago. For over a century, this corridor was dominated by four major railroads, and an aggregate of other roads that served as a fifth option.
New York Central Railroad
The first New York-Chicago route was provided on January 24, 1853 with the completion of the Toledo, Norwalk and Cleveland Railroad to Grafton, Ohio on the Cleveland, Columbus and Cincinnati Railroad. The route later became part of the Lake Shore and Michigan Southern Railway, owned by the New York Central Railroad.
Pennsylvania Railroad
In 1857, the Fort Wayne Railroad Bridge was completed across the Allegheny River in Pittsburgh, Pennsylvania, and trains began to run from Philadelphia to Chicago along the Pennsylvania Railroad and Pittsburgh, Fort Wayne and Chicago Rail Road (later part of the PRR).
The Connecting Railway in Philadelphia opened for revenue service on June 3, 1867, with direct service between Philadelphia and Jersey City, New Jersey, across the Hudson River from New York. Through freight between Jersey City and Pittsburgh began the next month, and soon some trains began running between Jersey City and Chicago.
Erie Railroad
The Erie Railroad Company was originally made to connect New York and Lake Erie. In 1941 they expanded to Chicago by merging with NYPANO RR.
Baltimore and Ohio Railroad
From its original charter terminus of Wheeling, West Virginia, reached in 1853, the Baltimore and Ohio Railroad pushed west by construction of new rails and by leasing other pre-existing ones. The B&O had reached Newark, Ohio by 1866, Sandusky by 1869, and had built a new line west into Chicago by 1874.
Alphabet Route
"Alfabet Route" referred to a series of railroads linking Chicago with Baltimore on the East Coast. From West to East this route comprised: Nickel Plate Road (NKP, or New York, Chicago & St. Louis Railroad) going east from Chicago, connecting with what formerly had been the Wheeling and Lake Erie Railroad (acquired by the NKP in late 1940s), and next the Pittsburg and West Virginia Railroad (P&WV), and finally the Western Maryland Railroad (WM). Again from Chicago, the original Nickel Plate line went to the Cleveland area, from whence the NKP/former Wheeling & Lake Erie went into southeastern Ohio at the West Virginia border to meet the P&WV, which in turn went across SW Pennsylvania to meet the Western Maryland RR at Connellsville PA. Finally, the Western Maryland carried traffic to Baltimore MD. This was a through route only for freight traffic, not for passenger service. I do not know if the term "Alfabet Route" was used prior to the NKP taking over the Wheeling.