Convolutional Neural Networks (CNN) have been widely adopted in multi-access edge computing system due to their powerful feature extraction and high inference accuracy. Harnessing the heterogeneous computational capacities of end de vices and edge servers, end-edge collaborative inference addresses resource constraints of end devices and latency challenges of real time inference. However, existing studies typically assume that all potential inference models are pre-employed on the server, which may not always align with real-world deployment scenarios. Moreover, the economic incentives of edge service providers are often overlooked in current distributed inference research. To address these issues, we propose an end-edge collaborative inference framework for CNN in multi-access edge computing system, named DisCNN. We first model the interaction between latency-sensitive end devices (EDs) and resource-constrained edge service providers as a Stackelberg game and prove the existence of a Subgame Perfect Equilibrium. Next, we derive the optimal response characteristics of the EDs and develop an efficient algorithm to allocate computation and communication resources to EDs while partitioning the CNN accordingly. To compute the optimal offloading set, we introduce a linear-time algorithm with a bounded approximation ratio. Then, to jointly optimize caching, resource allocation, and pricing, we design an efficient approximate algorithm to compute a near-optimal solution. Finally, extensive simulation results validate the effectiveness of the proposed framework.