This is the Extended / Alternated version Cold War, Enjoy!
In this scene where Spider-Man is shown in a free fall dive and starts to web swing throughout the city. Once Spider-Man gets word of a police chase, as a truck carrying plutonium from Oscorp has been hijacked, Spider-Man jumping on cars. While chasing the stolen truck, many cars are hit as a result. Max Dillion, carrying important blueprints for Oscorp, is bumped into by careless pedestrians and drops what he's carrying. As he tries to pick them up, a few fall right in the street as a car is flying by in the air. Spider-Man tells everyone to watch out as he saves Max just in time. Spider-Man addresses Max by name and Max asks him "How do you know my name?" Spider-Man says "Your badge, Oscorp." and fixing Max's hair, Spider-Man yells "You're my eyes and ears out here! I'll see you out there!" which excites Max, since he is a big Spider-Man fan. After making several jokes towards Alexei Sytsevich, the several tubes of plutonium start to fall out the back of the truck as Spider-Man catches them one by one. After retrieving all of them, one drops and starts to bounce around the city. He catches it as it lands in the street, getting hit and sticking to a car. While on the car, Gwen calls him to remind him to hurry up, because their graduation is about to start and she is about to give her speech. He tells Gwen that he is five to ten minutes from getting there since he is "stuck in traffic".
Audio: SUV Chase - John Powell (Hancock) Truckzilla - Marco Beltrami (A Good Day To Die Hard) Ballad In The City - Michael McCuistion (Spider-Man 2: The Game) Bikers - Lalo Schifrin (Rush Hour 3) Berlin Foot Chase - John Powell (The Bourne Supremacy) Main Titles - Don Davis (The Matrix Revolutions)
Extended/Alternate Scene from The Amazing Spider-Man 2 Director's Cut