Appeals from judgments against persons deprived of their liberty in cases of habeas corpus, and from judgment on informations in the nature of quo warranto to try the right to a public office, whether state, district, county, or municipal, and in actions of mandamus where the public interest is concerned, and in cases at law or in chancery involving taxes claimed by the state, county, or municipality, may be returnable before the Supreme Court immediately, without reference to the return days for other appeals; and when the transcript of the record of the case shall be filed in the office of the clerk of the Supreme Court, the appellee having been summoned to appear and answer the appeal, ten days after service of the summons on him or his attorney, the court shall consider such cases as entitled to be heard without regard to the district from which they are brought, and in preference to all civil cases, and they shall be heard and disposed of with all convenient speed.