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Online advertising driven by auctions brings billions of dollars in revenue for social networking services and e-commerce platforms. GSP auctions, which are simple and easy to understand for advertisers, have almost become the benchmark for ad auction mechanisms in the industry. However, most GSP-based industrial practices assume that the user click only relies on the ad itself, which overlook the effect of external items, referred to as externalities. Recently, DNA has attempted to upgrade GSP with deep neural networks and models local externalities to some extent. However, it only considers set-level contexts from auctions and ignores the order and displayed position of ads, which is still suboptimal. Although VCG-based multi-slot auctions (e.g., VCG, WVCG) make it theoretically possible to model global externalities (e.g., the order and positions of ads and so on), they lack an efficient balance of both revenue and social welfare. In this paper, we propose novel auction mechanisms named Neural Multi-slot Auctions (NMA) to tackle the above-mentioned challenges. Specifically, we model the global externalities effectively with a context-aware list-wise prediction module to achieve better performance. We design a list-wise deep rank module to guarantee incentive compatibility in end-to-end learning. Furthermore, we propose an auxiliary loss for social welfare to effectively reduce the decline of social welfare while maximizing revenue. Experiment results on both offline large-scale datasets and online A/B tests demonstrate that NMA obtains higher revenue with balanced social welfare than other existing auction mechanisms (i.e., GSP, DNA, WVCG) in industrial practice, and we have successfully deployed NMA on Meituan food delivery platform.