  We classify embedded blowups of the real affine plane up to oriented
isomorphy. We show that two blowups in the same isomorphism class are isotopic,
using a matrix deformation argument similar to an idea given by Shastri. This
answers two questions which were motivated by the interactive visualizations of
such blowups (see the work of the first author in [Elemente der Mathematik 50
(1995) 149-163] and the second author and Stussak in [IEEE Transactions on
Visualization and Computer Graphics 19 (2013) 978-990] and the references
there).
