The carbon transfers caused by inter-provincial commodity flows account for about 35 % of the total carbon emissions in China. There are great differences between the production-side and consumption-side carbon emissions for each province. Therefore, under the constraints of carbon peak and carbon neutralization, bilateral carbon emissions management is crucial to mitigate carbon emissions and the driving forces of bilateral carbon emissions must first be identified. Based on China's inter-provincial input-output data and carbon emissions data released by China Emissions Accounts and Datasets (CEADs), this paper uses a multi-regional input-output model (MRIO) to calculate the bilateral carbon emissions in 30 China's provinces from 2007 to 2017 and then apply structural decomposition analysis (SDA) to measure the influencing factors of these emissions. We also use counterfactual analysis to investigate the adjustment of provincial responsibilities for carbon emissions. The results show that the provinces in central and northern China undertake major net carbon inflows from other provinces in the eastern and southern coastal region. According to the results of SDA, the technological effect is an important factor in curbing the bilateral carbon emissions and the demand effect promotes the bilateral carbon emissions, but their contribution rates show a downward trend. By contrast, the variation in structural effect has significantly restrictive effects on the bilateral carbon emissions. Based on the provincial contribution to emissions mitigation, the adjusted consumption-side carbon emission embodies the principle of "more emission reduction, more compensation". We suggest implementing differentiated bilateral carbon emission management, taking the adjusted consumption-side carbon emission as the evaluation standard, and promoting inter-provincial carbon compensation.