Angiogenesis is the process of new blood vessels growing from existing vasculature. Visualizing them as a three-dimensional (3D) model is a challenging, yet relevant, task as it would be of great help to researchers, pathologists, and medical doctors. A branching analysis on the 3D model would further facilitate research and diagnostic purposes. In this paper, a pipeline of vision algorithms is elaborated to visualize and analyze blood vessels in 3D from formalin-fixed paraffin-embedded (FFPE) granulation tissue sections with two different staining methods. First, a U-net neural network is used to segment blood vessels from the tissues. Second, image registration is used to align the consecutive images. Coarse registration using an image-intensity optimization technique, followed by finetuning using a neural network based on Spatial Transformers, results in an excellent alignment of images. Lastly, the corresponding segmented masks depicting the blood vessels are aligned and interpolated using the results of the image registration, resulting in a visualized 3D model. Additionally, a skeletonization algorithm is used to analyze the branching characteristics of the 3D vascular model. In summary, computer vision and deep learning is used to reconstruct, visualize and analyze a 3D vascular model from a set of parallel tissue samples. Our technique opens innovative perspectives in the pathophysiological understanding of vascular morphogenesis under different pathophysiological conditions and its potential diagnostic role.