Relay nodes...
VZW doesn't have relay nodes, but they have made extensive use of microwave backhaul for their LTE network. For 3G (EVDO gets 3.1mbps max in one 1.25mhz channel) as far as I know Verizon made minimal or no use of wireless backhaul for this buildout. When I first started using 3G, I'd go to plenty of rural areas and find a top speed of 1.5mbps, i.e. probably a T1 running to it (and later I think 2 T1s.) This was fine for 3G (at least it would guarantee 1mbps or so most of the time) but clearly wouldn't do for LTE. In cities there's all this fiber, metro ethernet, etc., up and they can probably get nice backhaul to most sites. Otherwise they've run backhaul where they can and used microwave for quite a few LTE sites.
They also have a few "extra" links as failsafes; I read last year they had a fiber line get cut in Alabama (or maybe it was Arkansas?), it took down their cell and data service for like a quarter of the state, for about 5 minutes. It took until the next day to fix the fiber, but they just "flipped the switch" and put all the traffic over the microwave link that spanned the break. The article said they had just installed the new microwave backhaul within the past few weeks, and had been planning to turn on automatic failover in a few weeks.