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Mapping-based cross-domain recommendation (CDR) can effectively tackle the cold-start problem in traditional recommender systems. However, existing mapping-based CDR methods ignore data-sparse users in the source domain, which may impact the transfer efficiency of their preferences. To this end, this paper proposes a novel method named Neighbor Interaction-based Personalized Transfer for Cross-Domain Recommendation (NIPT-CDR). This proposed method mainly contains two modules: (i) an intra-domain item supplementing module and (ii) a personalised feature transfer module. The first module introduces neighbour interactions to supplement the potential missing preferences for each source domain user, particularly for those with limited observed interactions. This approach comprehensively captures the preferences of all users. The second module develops an attention mechanism to guide the knowledge transfer process selectively. Moreover, a meta-network based on users' transferable features is trained to construct personalised mapping functions for each user. The experimental results on two real-world datasets show that the proposed NIPT-CDR method achieves significant performance improvements compared to seven baseline models. The proposed model can provide more accurate and personalised recommendation services for cold-start users. [ABSTRACT FROM AUTHOR]