Battle: Los Angeles

The Giants and Jets have always played at 1:00.
Until 2011, they had always played at 1:00 on a Sunday, but in 2011 they played on a Saturday.
Until 2015, they had always played at 1:00 on the doubleheader network, but in 2015 they played on the singleheader network.
Regardless, they've still always played at 1:00.

With the Chargers and Rams starting their in-city rivalry today, they are playing at 1:05 on a Sunday on the singleheader network. I'll keep note of that to see if it remains the same moving forward, as the Giants and Jets have always done.