  In this contribution, quasi-orthogonality of polynomials generated by
Geronimus and Uvarov transformations is analyzed. An attempt is made to discuss
the recovery of the source orthogonal polynomial from the quasi-Geronimus and
quasi-Uvarov polynomials of order one. Moreover, the discussion on the
difference equation satisfied by quasi-Geronimus and quasi-Uvarov polynomials
is presented. Furthermore, the orthogonality of quasi-Geronimus and
quasi-Uvarov polynomials is achieved through the reduction of the degree of
coefficients in the difference equation. During this procedure, alternative
representations of the parameters responsible for achieving orthogonality are
derived. One of these representations involves the Stieltjes transform of the
measure. Finally, the recurrence coefficients ensuring the existence of a
measure that makes the quasi-Geronimus Laguerre polynomial of order one an
orthogonal polynomial are calculated.
