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In the present work, we study the decompositions of codimension-one transitions that alter the singular set the of stable maps from S3 to R3, the topological behaviour of the singular set and the singularities in the branch set that involves cuspidal curves and swallowtails that alter the singular set. We also analyse the effects of these decompositions on the global invariants with prescribed branch sets. © 2019, Sociedade Brasileira de Matemática.

We greatly acknowledge Mr. Daniel Gómez for the technical assistance with the animals. The skillful work Mr. Fructuoso Cuentas on the maintenance of the P50 equipment donated by the International Foundation for Science (IFS) is also gratefully acknowledged. This work was supported in part by the “Consejo Nacional de Ciencia y Tecnolog??a” (CONCYTEC) Lima—Perú, the Institut Francais d'Etudes Andines (IFEA) and the IFS.

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We greatly acknowledge BSc Rosario Tapia for thetechnical assistance with the animals. This work wassupported in part by the Consejo Nacional de Ciencia yTecnologia (CONCYTEC) Lima, Perú, the InstitutFranc ̧ais d’Etudes Andines (IFEA), Lima and the San-doz Laboratories, Rueil, France.

We wish to thank Centro de Referencia para Lactobacilos (CERELA-CONICET) collection for supplying the strains. We would also like to thank IBRAC and Sealed Air-Brazil that provided the additives and packaging, respectively. M. Almeida received the support of the Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES), PhD scholarship from Brazil and E. Saldaña received the support of the “Consejo Nacional de Ciencia, Tecnología e Innovación Tecnológica - CONCYTEC” from Perú (CIENCIACTIVA programme, PhD scholarship contract agreement No. 104-2016-FONDECYT). This study was financially supported by the São Paulo Research Foundation (FAPESP) Project No.2012/07113-2; project AGL2012-32146 from MINECO (Spain) and PIP2011-0100406 and PIP2015-0530 from CONICET.