Whenever there is a need to sponsor a foreign worker on visa to his Green Card, US govt requires companies to make an attempt to hire a US citizen with similar skills. In order to get the green card application through the corporations are required to show a proof that the corporation tried to find a US citizen to fill the position. So for this the corporation orchestrates an interview sessions and documents them thoroughly to present it to US Govt. So all this openings that you see at Verizon are most likely all fake openings and if you applied you will waste your time through series of well documented interviews. The vz IT managers are so good at this federal crime they take those interviews like just another lunch. Most of the current IT leaders have gotten to the leadership with these fake interviews themselves so they probably think its a good practice.
So before you get excited about applying for a position at vz just remember that it might as well just be a fake hiring process.