Although the blueprint service has been used to analyze services using AI, it has not been used to characterize how a service changed as AI was increasingly used to change it. We propose a comparative case study design of the taxi service in France and USA at three stages of AI introduction, traditional taxi (zero AI), Uber (AI to improve the matchmaking between users and drivers), autonomous taxi (AI to book the taxi, find it, optimize the journey, and drive the taxi). For each case, we use the service blueprint tool to show how AI changes the user experience and the internal (front facing and backstage) of the service, to help companies better understand both the value AI can bring to user, and the corresponding changes it requires in terms of assets and process. We show how an improved service blueprint with lines for data and algorithms can help businesses successfully introduce AI. The results also underline the need to carefully consider emotional and social values in addition to functional ones, and go beyond eliminating pain points to also focus on creating surprising experiences.