Miniversal deformations of chains of linear mappings

V. I. Arnold [Russian Math. Surveys, 26 (no. 2), 1971, pp. 29–43] gave a miniversal deformation of matrices of linear operators; that is, a simple canonical form, to which not only a given square matrix $A$, but also the family of all matrices close to $A$, can be reduced by similarity transformations smoothly depending on the entries of matrices. We study miniversal deformations of quiver representations and obtain a miniversal deformation of matrices of chains of linear mappings
$$ V_1\,\frac{\qquad}{\qquad}\,V_2\,\frac{\qquad}{\qquad}\,\cdots\,\frac{\qquad}{\qquad}\,V_t\,, $$
where all $V_i$ are complex or real vector spaces and each line denotes $\longrightarrow$ or $\longleftarrow$.