The online grocery wars are heating up in the Big Apple, with service to shoppers now extending to every last neighborhood.

Peapod, a food-delivery site that’s owned by the parent of Stop & Shop, has expanded its coverage area to every ZIP code in all boroughs, The Post has learned.

Backed by the buying clout of Netherlands-based Ahold, Peapod is widening its footprint as it goes head-to-head in the city with rivals like FreshDirect, Instacart, Amazon and Delivery.com.

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