National Hockey League games between the New York Islanders and the New York Rangers have been called the “Battle of New York.” The term “Battle of New York” has been especially popular when the two teams face each other in a playoff series, as they first did in April 1975.
 
“If all three Islander newcomers can duplicate their outstanding play Sunday against the Rangers at Madison Square Garden, the battle of New York may become one of the biggest attractions in the NHL” was written by hockey writer Walt MacPeek in The Star-Ledger (Newark, NJ) on November 9, 1973. “In addition to trying to win the battle of New York for the Islanders, (Denis—ed.) Potvin had other goals set for his rookie year” was written by UPI’s Martin Lader in the Ottawa (ON) Journal on March 16, 1974. “The Rangers, who travel to Atlanta tomorrow night (Ch. 9 at 8:00), increased their advantage in the continuing hockey ‘Battle of New York’ to 13-1-1 overall and 7-0-1 at Madison Square Garden” was written by Walt MacPeek in The Star-Ledger (Newark, NJ) on March 13, 1975.
 
“The opening round pairing pit Los Angeles against Toronto; Chicago against Boston; St. Louis against Pittsburgh; and the Rangers against the Islanders in what will be remembered as the Battle of New York, 1975” was written by Don Wilno in The Evening Times (Trenton, NJ) on April 8, 1975.
     
     
Wikipedia: Islanders-Rangers rivalry
The Islanders–Rangers rivalry, also known as the Battle of New York, is a rivalry between the New York Islanders and New York Rangers of the National Hockey League. Both teams play in New York City, with the Rangers in the borough of Manhattan, and the Islanders in the borough of Brooklyn. They are two of the three teams that play in the New York metropolitan area, the other being the New Jersey Devils who play in Newark, New Jersey. The rivalry is an intra-city rivalry similar to the Mets–Yankees rivalry in Major League Baseball and join the recent Knicks–Nets rivalry and yesteryear’s Dodgers–Giants rivalry as professional sports rivalries between teams based in New York City’s most populous borough, Brooklyn, and the location of most of New York’s corporate headquarters and shopping districts, Manhattan.
           
9 November 1973, The Star-Ledger (Newark, NJ), “Breaking the Ice” by Walt MacPeek, pg. 44, col. 3:
If all three Islander newcomers can duplicate their outstanding play Sunday against the Rangers at Madison Square Garden, the battle of New York may become one of the biggest attractions in the NHL.
     
16 March 1974, Ottawa (ON) Journal, “Potvin looks forward to rivalry with Rangers” by Martin Lader (UPI), pg. 14, col2. 4-5:
In addition to trying to win the battle of New York for the Islanders, (Denis—ed.) Potvin had other goals set for his rookie year.
 
17 March 1974, Sunday Herald Advertiser (Boston, MA), “Potvin’s Private Gotham Mission—Overtake Rangers” (UPI), sec. 4, pg. 61, col. 6:
In addition to trying to win the battle of New York for the Islanders, (Denis—ed.) Potvin had other goals set for his rookie year.
 
11 March 1975, The Jersey Journal (Jersey City, NJ), “Harris to play against Bruins tonight” by Walter MacPeek, pg. 21, col. 7:
The Islanders, who lost at California Sunday night, hope to overtake the Rangers for second place in Division I and the “Battle of New York” figures to be a fierce one.
 
13 March 1975, The Star-Ledger (Newark, NJ), “Beverley paces Rangers; Pin 5-3 loss on Islanders” by Walt MacPeek, pg. 63, col. 1:
The Rangers, who travel to Atlanta tomorrow night (Ch. 9 at 8:00), increased their advantage in the continuing hockey “Battle of New York” to 13-1-1 overall and 7-0-1 at Madison Square Garden.
 
8 April 1975, The Evening Times (Trenton, NJ),  “Crystal ball still cracked from last year, but” by Don Wilno, pg. 18, col. 4:
The opening round pairing pit Los Angeles against Toronto; Chicago against Boston; St. Louis against Pittsburgh; and the Rangers against the Islanders in what will be remembered as the Battle of New York, 1975.
 
11 April 1975, Pittsburgh (PA) Post-Gazette, pg. 14, col. 1:
Rangers Down Islanders
In Battle of New York
UNIONDALE, N. Y. (AP)—Bill Fairbairn scored twice within a 51-second span of the first period last night to lead the New York Rangers to a browling 8-3 victory over the New York Islanders, tieing their best-of-three first-round Stanley Cup series at one victory each.
   
Google Books
Kings of the Rink
By Stan Fischler
New York, NY: Dodd, Mead
1978
Pg. 89:
11 seconds into the overtime, J. P. Parise of the Islanders scored from close range, and the new kids from Nassau County had won “The Battle of New York.”
 
Google Books
New York Rangers
By Mark Everson
Mankato, MN: Creative Education
1996
Pg. 21:
The Rangers dropped the opener, then roared back to move into the semifinals — a renewal of the Battle of New York against the Islanders.
 
Twitter
Eyewitness News
@ABC7NY
Isles beat Rangers with short handed goals: In a battle of New York, the Islanders beat the Rangers.. http://tinyurl.com/6xt43p
9:48 PM - 4 Nov 2008
   
Google Books
100 Things Rangers Fans Should Know & Do Before They Die
By Adam Raider and Russ Cohen
Chicago, IL: Triumph Books LLC
2014
Pg. 40:
Despite opposition from the Rangers, who didn’t want or need competition from across the East River, the league granted an expansion team to Nets owner Roy Boe. The Battle of New York had begun.
 
Twitter
NHL
@NHL
The latest edition of the Battle of New York?
Victory: @NYIslanders
8:00 AM - 3 Dec 2015
     
Google Books
The Handy New York City Answer Book
By Chris Barsanti
Canton, MI: Visible Ink Press
2017
Pg. 314:
Rangers-Islanders games are sometimes referred to as the Battle of New York.
 
Twitter
The Battle of New York
@battleofny_
The Battle of New York is proud to debut our logo! We wanted to make a logo that’s modern and represents the Islanders and Rangers rivalry. Let us know what you think!
4:20 PM - 12 Feb 2019