Anarchist often times call themselves libertarian socialists or libertarian communists. In socialism you can own personal property and capital. But major industries that are used by the community will be unionized and democratized. Marxism is a thread of socialism, an opinion on how to get socialism, it is not socialism. Industrial unionism is far better, more peaceful, effective and democratic than marxism. Socialism and communism, when centralized, failed. You have to decentralize it and democratize, exactly what Marx and millions of other communists tried and are trying to do.