Can i get a nexus from google & connect it with Verizon??

No, the Nexus that is sold in the play store is the GSM version, and will not work with Verizon, because Verizon is CDMA. You have to get the Verizon specific Galaxy Nexus with Lte for it to work on Verizon. Hope this helps!
 
You should be able to get the Verizon Galaxy Nexus from Verizon itself off contract (I did). I have no idea what it costs at this point, but it could be pricey. I will say that maintaining my grandfathered unlimited data plan but not having a contract feels pretty darn good.
 
Verizon will charge full price. Your best bet is to buy used. I got a Verizon nexus off gazelle's eBay store for $260 in "very good" condition. There were other phones at $230 in lesser conditions. Obviously its not going to be new and your mileage will vary, but if you want to keep unlimited data or hold yourself over till a new nexus comes out, its the cheapest option.

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