The phrase "obvious appearance" refers to something that is easily noticeable or clearly seen without much effort. It means that the way something looks is very apparent or unquestionable. Full definition
Luther even extolled the religious value of housework, declaring that although «it has no obvious appearance of holiness, yet these very household chores are more to be valued than all the works of monks and nuns.» (firstthings.com)
Cameron 2010, 36.1, 306 seats, gained premiership Blair 2005, 35.2 %, 355 seats, retained premiership Despite the obvious appearance of the system being progressively rigged in Labour's favour between 1979 and 2010 (and while LIberal support almost doubled), Cameron still got into No. 10. (nextleft.org)
There is an obvious appearance of corruption and graft given the relationship between Achievement First and State Commissioner of Education Stepfan Pryor. (jonathanpelto.com)