  We introduce three new analytical and semi-analytical tools that allow one to
determine the topological character of impurity Shiba chains. The analytical
methods are based on calculating the effective Green's function of an infinite
embedded chain using the T-matrix formalism and describing the chain as a {\it
line impurity}. We thus provide a solution to the longstanding size-effects
problem affecting the only general alternative method, the numerical
tight-binding analysis. As an example we consider a chain of magnetic
impurities deposited on an s-wave superconducting substrate with Rashba
spin-orbit and we calculate its topological phase diagram as a function of the
magnetic impurity strength and the chemical potential. We find a perfect
agreement between all our new techniques and a numerical analysis.
