(a) The right of a person who has been convicted of a public offense to a new trial or to an appeal from the judgment of conviction shall not be affected by anything in this chapter.
(b) When a person who has been convicted and committed to the Authority appeals from the conviction, the execution of the commitment to the Authority shall not be stayed by the taking of the appeal except as provided in subsection (c). The person so committed shall remain subject to the control of the Authority, until final disposition of the appeal.
(c) A person convicted and committed to the Authority may be admitted to bail under the provisions of Section 1272 of the Penal Code, or in the discretion of the court, may be left at liberty, under such conditions as in the court’s opinion will insure his cooperation in reasonable expedition of the appellate proceedings and his submission to the control of the Authority at the proper time.