stay in either side of the street vs stay on either side of the street

Some examples from the web:

• If we stay on these side streets.
• I want you to clear all the civilians from either side of the street.
• Two trees, either side of the path.
• There are three dozen cosponsors on either side of the aisle.
• Keep the person on either side of you within sight.
• Rub either side of your jaw, to release the tension.
• Two guys packing either side of us, Mikey.
• Two knots on either side of the wire.
• The lacerations either side of the neck were more or less symmetrical.
• So there's two cones on either side of the goal.
• There's two goals, one on either side of the court.
• Why? Machinegun nests either side of the rear gate.
• They should be on either side of you.
• - running on either side of Willet Creek.
• You got stairwells on either side of the building.
• The farms are 5 km apart on either side of the border.
• Put those chairs on either side of the door.
• Everyone's eyes should stay at a specific vector - angle - on either side of the trail.
• One smart kid makes their work visible for the cheats slipstreaming either side of them.
• Two round blood smears on either side of her, - so the killer was kneeling over her.

Some examples from the web:

• If we stay on these side streets.
• There are three dozen cosponsors on either side of the aisle.
• Keep the person on either side of you within sight.
• Two knots on either side of the wire.
• So there's two cones on either side of the goal.
• There's two goals, one on either side of the court.
• They should be on either side of you.
• - running on either side of Willet Creek.
• You got stairwells on either side of the building.
• The farms are 5 km apart on either side of the border.
• Put those chairs on either side of the door.
• Everyone's eyes should stay at a specific vector - angle - on either side of the trail.
• Two round blood smears on either side of her, - so the killer was kneeling over her.
• This amendment takes into account that congestion can also arise within the transmission networks on either side of the interconnections.
• You don't have any friends, Ayla, on either side of the fence.
• Lay her inside the salt and lie on either side of her.
• Please, thank all of your wives for the heartiest hospitality I have felt on either side of the Mississippi.
• So there we are, resting our hands on either side of the divide.
• The bills with serial numbers on either side of the money you found are circulating in central Maryland.
• So, I'm seeing two rods on either side of the spine to preserve nerve root function.