Comparing time surfaces at different integration time points, or from different seeding areas, can provide valuable insight into transport phenomena of fluid flows. Such a comparative study is challenging due to the often convoluted shapes of these surfaces. We propose a new approach for comparative flow visualization based on time surfaces, which exploits the idea of embedding the surfaces in a carefully designed, reformed 2D visualization space. Such an embedding enables new opportunities for comparative flow visualization. We present three different strategies for comparative flow visualization that take advantage of the reformation. By reforming the time surfaces, we not only mitigate occlusion issues, but we can devote also the third dimension of the visualization space to the comparative aspects of the visualization. Our approach is effective in a variety of flow study cases. The direct comparison of individual time surfaces reveals small scale differences and fine details about the fluid's motion. The concurrent study of multiple surface families enables the identification and the comparison of the most prominent motion patterns. This work was developed in close collaboration with an expert in fluid dynamics, who assessed the potential usefulness of this approach in his field.